Find sin(B).
1. a/b

2. a/c

3. b/a

4. b/c


5. c/a


6. c/b

x2−1x5=(x−a)2+b2−15=(−)2+

The horizontal asymptote   of  the given function is 0

Given the function y = 19800/x

Vertical asymptote occurs at when f(x) = 0 where;

f(x) is the denominator of the given function.

From the expression given: f(x) = x

Since f(x) => 0, hence x = 0

To get the horizontal asymptote, we will look at the degree of the numerator and denominator.

If the degree of numerator is less than the denominator,

the horizontal asymptote will be zero. From the function, we can see that the degree of the numerator is zero (being a constant) and that of the denominator is 1.

Since 0<1, hence the horizontal asymptote is 0

x = 0, y = 0

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The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.

The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.

In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.

The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.

The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.

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The probability of picking a prime number is 2/3 or approximately 0.667.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Out of the given options of 2, 3, and 4, only 2 and 3 are prime numbers. Therefore, the probability of picking a prime number is:

P(prime) = number of prime options / total number of options

P(prime) = 2/3

So the probability of picking a prime number is 2/3 or approximately 0.667.

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A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.

A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.

By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.

Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"

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Answer:

We can use the formula for compound interest to calculate the amount of interest Brian will earn:

A = P (1 + r/n)^(nt)

where:

A = the total amount after 7 years

P = the principal amount ($9,411)

r = the annual interest rate (3.48%)

n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)

t = the number of years (7)

Plugging in the values, we get:

A = $9,411 (1 + 0.0348/52)^(52*7)

A = $9,411 (1.0006692302021135)^364

A = $12,471.36

To find the amount of interest earned, we can subtract the principal amount from the total amount:

Interest = $12,471.36 - $9,411 = $3,060.36

Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.

Answer:

64π

Step-by-step explanation:

Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.

The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.

Mathematically, the area of a circle can be calculated by using this formula:

[tex]\text{Area} = \pi \text{r}^2[/tex]

Where:

[tex]\text{r}[/tex] represents the radius of a circle.

[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]

By substituting the radius into the formula for the area of a circle, we have the following;

[tex]\text{Area of circle} = \pi \times 8^2[/tex]

[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.

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Answer: there is no solution

Step-by-step explanation:

The solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

The general form of the quadratic equation is: ax² + bx + c = 0

Given that, a quadratic equation (x-5)² + 3(x-5) + 9 = 0, we need to solve it,

So, put x-5 = u

Therefore,

u² + 3u + 9 = 0

Solving using quadratic formula,

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}[/tex]

Here a = 1, b = 3 and c = 9

Therefore,

[tex]u=\frac{-3 \pm \sqrt{3^2-4(9)}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{9-36}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{-27}} {2}[/tex]

[tex]u=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

Put u = x-5,

Therefore,

[tex]x-5=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

[tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Hence, the solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

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Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.

To estimate the area under the curve of the function f(x) = x3 between the limits of integration a=0 and b=3, we must divide the interval [0, 3] into three subintervals of equal width.

Each subinterval's width, x, may be calculated as follows:

Δx = (b - a) / n = (3 - 0) / 3 = 1

So, the three subintervals are:

[0, 1], [1, 2], [2, 3]

To compute the right-hand total, we evaluate the function at each subinterval's right endpoint and multiply it by the breadth of the subinterval. Then we add these products together to calculate the area under the curve. The right-hand sum may be stated mathematically as follows:

RH = Δx * [f(1) + f(2) + f(3)]

where x represents the width of each subinterval, f(x) = x3 represents the function we are integrating, and f(i) represents the function's value at the right endpoint of the i-th subinterval.

RH = 1 * [f(1) + f(2) + f(3)]

= 1 * [(1³) + (2³) + (3³)]

= 1 * [1 + 8 + 27]

= 36

Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

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Emilee will spend around $3,726 for her wrist surgery once her insurance company pays 70% and she meets the $371 deductible.

Calculating out-of-pocket costs for a medical expense after insurance coverage and deductibles often requires simple arithmetic.

To begin, deduct the deductible from the overall cost of the surgery: $12,791 - $371 = $12,420.

70% of the remaining cost after the deductible is calculated as follows: 70% of $12,420 = $8,694.

Total cost after insurance coverage: $12,420 - $8,694 = $3,726

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The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

The operation we are to carry out is:

Add -4(row 1) to row 3

This essentially means we should multiply the first row (row 1) by -4. Then, we will add each of the elements from the results to the corresponding elements on the third row

Multiplying by -4

-4 × [ 1     2    1   | -5

      -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

    4    -1     6  |  -8

+  -4   -8   -4  | 20

------------------------

    0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

The value of angle B and C are 63° and 61° respectively.

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore;

32/sin56 = 34/sinC

32sinC = 34sin56

32sinC = 28.187

divide both sides by 32

sinC = 28.187/32

sinC = 0.88

C = sin^-1(0.88)

C = 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore, B = 180-(61+56)

B = 180-(117)

B = 63°

therefore the value of angle B and C are 63° and 61°.

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The value after solving mixed fraction is 32/10=3.2

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.

according to question,

=51/10 - 19/10

=32/10

=3.2

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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.

To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.

5 1/10 can be converted to an improper fraction as follows:

5 1/10 = (5 x 10 + 1)/10 = 51/10

1 9/10 can be converted to an improper fraction as follows:

1 9/10 = (1 x 10 + 9)/10 = 19/10

Now we can subtract the two fractions:

51/10 - 19/10 = (51 - 19)/10 = 32/10

32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.

So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

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The  polynomial with integer coefficients and a leading coefficient of 1  is (x-6) (x-3)²  which in turn will be: f(x) = x³ - 12x² + 45x - 54

Based on the question, If the zeros of a polynomial are said to be 6, 3, and 3, one can say that the polynomial can be written in factored form such as

f(x) = (x - 6)(x - 3)(x - 3)

The to solve this, we have to multiply it:

f(x) = (x - 6) (x² - 6x + 9)

f(x) = x³ - 6x² + 9x - 6x² + 36x - 54

f(x) = x³ - 12x² + 45x - 54

Therefore, the polynomial with integer coefficients and a leading coefficient of 1  will be f(x) = x³ - 12x² + 45x - 54

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The volume of the composite solid is  452. 160 ft³

First, it is important to note that the formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters of the formula are;

From the information given,

substitute the values

Volume = 3.14 × 6² × 12/3

Divide the values

Volume = 31.4 × 36 × 4

Multiply the values

Volume = 452. 160 ft³

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the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

How to solve the question?

To determine the scale factor used in the dilation of triangle D to create triangle D', we need to compare the corresponding sides of both triangles. The corresponding sides of two similar triangles are proportional, meaning that they have the same ratio.

In this case, we can see that the length of every side of triangle D' is one-third the length of the corresponding side of triangle D. For example, the length of the shortest side of triangle D is 18, while the length of the shortest side of triangle D' is 6. Similarly, the length of the longest side of triangle D is 30, while the length of the longest side of triangle D' is 10.

We can use this information to find the scale factor by dividing the length of any side of triangle D' by the length of the corresponding side of triangle D. Let's choose the shortest side for this calculation:

scale factor = length of corresponding side in D' / length of corresponding side in D

scale factor = 6 / 18

scale factor = 1/3

Therefore, the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

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A statistical question would be:  What is the average salary of teachers in this school district?

When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.

A statistical question would be:  What is the average salary of teachers in this school district?

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On solving the provided question we can say that area of the polygon is 24 cm sq.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Area of this polygon is -

A = 1/2 * 6* 8

A = 24 cm sq.

Hence, area of the polygon is 24 cm sq.

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Answer:

38 inches

Step-by-step explanation:

We can use the Law of Sines to solve for the length of side g:

sin(66°)/67 = sin(30°)/g

Cross-multiplying, we get:

g*sin(66°) = 67*sin(30°)

Dividing both sides by sin(66°), we get:

g = 67*sin(30°)/sin(66°) ≈ 38 inches (rounded to the nearest inch)

Therefore, the length of side g is approximately 38 inches.

Psychologist requires a sample size of at least 126 SI scores.

We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:

[tex]n = [Z * (\sigma / E)]^2[/tex]

Where:

Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.

For a 90% confidence level, Z is approximately 1.645.

σ = the population standard deviation (82)

E = the desired margin of error (12)

Plugging in the values, we get:

n = [1.645 * (82 / 12)]^2

n = 126.2

We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.

Thus, n = 126 is the required minimum sample size.

In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.

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Answer:

Let's call the unknown number "x". According to the problem, we know that:

x * (x - 6) = 27

Expanding the left side of the equation, we get:

x^2 - 6x = 27

Subtracting 27 from both sides, we get:

x^2 - 6x - 27 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -6, and c = -27, so:

x = (-(-6) ± sqrt((-6)^2 - 4(1)(-27))) / 2(1)

x = (6 ± sqrt(180)) / 2

x = (6 ± 6sqrt(5)) / 2

x = 3 ± 3sqrt(5)

So the two possible solutions are:

x = 3 + 3sqrt(5) ≈ 8.746

x = 3 - 3sqrt(5) ≈ -2.746

Since the problem statement doesn't specify whether the number should be positive or not, both solutions are valid.

Answer: The answer could be 9 or -3.

Step-by-step explanation: The product(multiply) of a number(x) and 6 less than a number(x-6) is 27.

x(x-6)=27

x^2-6x-27=0

(x-9) (x+3)=0

x=9 or x=-3

The number is 9 or -3.

The variables are as follows:

x = 4

y = 4.8

The lengths of the sides of the kites are 4.5 and 6.8 units.

A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.

The non vertex angles are congruent.

Therefore,

x + 0.5 = 2x - 3.5

2x - x = 0.5 + 3.5

x = 4

y + 2 = 2y - 2.8

2y - y = 2 + 2.8

y = 4.8

Hence,

length of one pair = 4 + 0.5 = 4.5 units

length of the other pair = 4.8 + 2 = 6.8 units

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Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.

Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.

We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):

We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:

cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²

Using the scale factor equation for height, we get:

k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31

Using the scale factor equation for cross-sectional area, we get:

k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)

Solving for the cross-sectional area of Prism B, we get:

cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]

Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:

Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]

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Therefore, we estimate that there are 2250 Art majors in the total population.

In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.

Here,

We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.

The proportion of Art majors in the sample is:

75/250 = 0.3

We can assume that this proportion is representative of the proportion of Art majors in the population.

So, if x is the total number of Art majors in the population, then we can set up the following proportion:

0.3 = x/7500

To solve for x, we can cross-multiply and simplify:

0.3 * 7500 = x

x = 2250

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Answer:

2/15 litre

Step-by-step explanation:

There is 1 litre in total. Max used 1/5 litre.

1 - 1/5 = 4/5 litre

Then he used 5/6 of the remaining 4/5 litre. He would have 1/6 of 4/5 litre left.

1/6 * 4/5 = 2/15 litre

or

You could do 5/6 * 4/5 to find out how much syrup he used on Sunday and then subtract that from 4/5 litre. It will give you the same answer

Answer: 2

Step-by-step explanation:

We can simplify the given logarithmic expression using the logarithmic property that states:

log a base b - log c base b = log (a/c) base b

Using this property, we can rewrite the expression as follows:

log 16 base 2 - log 4 base 2 = log (16/4) base 2

Simplifying the numerator of the logarithm, we get:

log (16/4) base 2 = log 4 base 2

Now, we can evaluate the logarithm using the definition of logarithm, which states that:

log b base a = x if and only if a = b^x

In this case, we have:

log 4 base 2 = x if and only if 2^x = 4

We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.

Therefore, we have:

log 4 base 2 = 2

Hence, the value of the given logarithmic expression is 2.