2 ^ x = 3 ^ (x + 1) solve for x
Answers
Answer:
-2.71
Step-by-step explanation:
This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.
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solve for x2^x = 3^(x+1) . . . . . given
2^x = 3·3^x . . . . . . eliminate the constant in the exponent
(2/3)^x = 3 . . . . . . . divide by 3^x
x·log(2/3) = log(3) . . . . take logarithms
x = log(3)/log(2/3) ≈ -2.7095113
The value of x is about -2.71.
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Alternate solution
Taking logarithms transforms this exponential equation to a linear equation.
x·log(2) = (x +1)·log(3) . . . . take logs
x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)
x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above
_____
Additional comment
In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
Related Questions
Which statements describe organic compounds
1+1
Answers
Organic compounds are commonly found in living things.
Organic compounds contain carbon.
Organic compounds are found in food.
What are the properties of organic Compounds?Organic compounds are defined as compounds that consist of groups of carbon atoms covalently bonded to hydrogen, oxygen, and sometimes other elements too.
Now, organic compounds are created by living things and so they are found throughout the world, in soils and seas, commercial products, and every cell of the human body.
Looking at the options and comparing to the definition above, only options A, C and E are correct.
The missing options are;
Organic compounds are commonly found in living things.
Organic compounds are not associated with or made from living things.
Organic compounds contain carbon.
Organic compounds usually lack carbon.
Organic compounds are found in food.
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Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
Answers
[tex]y^{-8} y^3 x^0 x^{-2}[/tex] is equivalent to [tex]y ^{-5} x ^{-2}\\[/tex].
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]y^{-8} y^3 x^0 x^{-2}[/tex]
Simplify
[tex]y^{-8} y^3 x^0 x^{-2}\\\\y ^{-8+3} x ^{0-2}\\ \\y ^{-5} x ^{-2}\\[/tex]
Hence, [tex]y^{-8} y^3 x^0 x^{-2}[/tex] is equivalent to [tex]y ^{-5} x ^{-2}\\[/tex].
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A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
Answers
The formula in factored form is (t - 3)(t - 9) and the swimmer dives into the water 3 seconds after the timer was started also, the swimmer comes back up 9 seconds after the timer was started.
Analysis:
at h(t) = 0 that is when the diver has not dived or at height 0 foot
the equation becomes [tex]t^{2}[/tex] -12t + 27 = 0
by factorizing,
[tex]t^{2}[/tex] -9t -3t + 27 = 0
(t-9)(t-3) = 0, this is the equation in factored form.
t = 3 or 9
These are the times, the height h(t) = 0
Which means the swimmer dived 3 seconds later or got to the top of water after 9 seconds in which case h(t) = 0
In conclusion, the swimmer dives 3 seconds later after the timer was started and the swimmer comes back up after 9 seconds are the true statements for this problem.
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Answer:
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives into the water 3 seconds after the timer was started.
Step-by-step explanation:
What is the approximate area
Answers
Answer:
2827.43in²
Step-by-step explanation:
formula for area of a circle is r²π with r being the radius (30 in this case)
we can plug in 30 for r to solve for the area
30²π
900π
2827.43
that is the answer
- kan academy advance
What is the equation of a line parallel to y=(3)/(4)x-5 and passes through (12,-2)?
Answers
A parallel line has the same slope as the original line. So in this case the slope of the line is also 3/4. Now how do we know if it intersects the point? We need to adjust the y intercept.
Currently, we know the equation of the line is y= 3/4 x + b, where b is the thing we are looking for. We also have a point, which supplies the x and y. Plug that in and solve for b
-2 = (3/4)*(12) + b
You'll get b= -11
So the equation of the parallel line intersecting the point given is y= 3/4x -11.
I am assuming that the slope is 3/4 based on the way you formatted the original equation, but it's the same steps if the slope is different.
Paula has buttons. she gives away 28 buttons. choose the expression that shows the number of buttons paula has left.
Answers
Answer:
y = 28 - x
Step-by-step explanation:
The variable x represents how many buttons Paula had before giving 28 away and the variable y represents how many buttons she has now.
Automobile insurance with the split limits 200/300/400 will cover up to how much in bodily injury per person?
Answers
Automobile insurance with the split limits 200/300/400 will cover up to $200,000 in bodily injury per person.
What is Insurance?This is a form of protection from financial loss and is used as a means of risk management.
$200,000 medical bodily injury coverage per person, $300,000 bodily injury coverage for the entire accident and $400,000 total property damage limits.
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What is the approximate length of AB¯¯¯¯¯¯¯¯?
Answers
Answer
9.2 units
Step-by-step explanation:
A(-2,-2) and B(4,4) then the length is given by the distance formula
length = [tex]\sqrt{(4-(-2))^{2}+(4-(-3))^{2} }[/tex] units
= [tex]\sqrt{6^{2}+7^{2} }[/tex] units
= [tex]\sqrt{85\\[/tex] units
= 9.2 units
Answer:
AB ≈ 9.2 units
Step-by-step explanation:
calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (- 2, - 3 ) and (x₂, y₂ ) = B (4, 4 )
AB = [tex]\sqrt{(4-(-2))^2+(4-(-3))^2}[/tex]
= [tex]\sqrt{(4+2)^2+(4+3)^2}[/tex]
= [tex]\sqrt{6^2+7^2}[/tex]
= [tex]\sqrt{36+49}[/tex]
= [tex]\sqrt{85}[/tex]
≈ 9.2 units ( to the nearest tenth )
Which pattern below does not follow the same rule as the other three patterns? A $2$ , $4$ , $8$ , $16$ , $32$ 2, 4, 8, 16, 32, B $5$ , $10$ , $20$ , $40$ , $80$5, 10, 20, 40, 80 C $15$ , $25$ , $35$ , $45$ , $55$15, 25, 35, 45, 55 D $25$ , $50$ , $100$ , $200$ , $400$
Answers
Answer:
C. 15, 25, 35, 45, 55
Step-by-step explanation:
Each number in A, B, and D are double the previous number but C adds 10.
mi
pie
In the following diagram, BC is parallel to DE.
What is the measure of Zz?
Angles are not necessarily drawn to scale.
B
C
4
103°
A
D
F
La=
42°
E
Answers
Answer: 35
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].
Sp, by the corresponding angles theorem, x=35
Find the value of x ..... Thanks
Answers
[tex]\dfrac{|AE|}{|AD|}=\dfrac{|AB|}{|AC|}[/tex]
Therefore:
[tex]\dfrac{10}{10+8}=\dfrac{x}{10}\\\\\dfrac{10}{18}=\dfrac{x}{10}\\\\18x=100\\x=\dfrac{100}{18}=5.555\ldots=5.\overline{5}[/tex]
So, none of the choices are correct (5.5 is an approximation).
Can somebody help me find the surface area
Answers
To calculate the area of the complex shape:
⇒ must separate the shape into simpler shape
2 rectangles with a length 9ft and a width 6ft1 rectangle with a length of 9 ft and a width 3ft2 triangles with a base of 3 ft and a height 5.4ftLet's calculate:
2 rectangles with a length 9ft and a width 6ft[tex]Area = 9*6+9*6=54+54=108[/tex]
1 rectangle with a length of 9 ft and a width 3ft[tex]Area= 9*3=27[/tex]
2 triangles with a base of 3 ft and a height 5.4ft[tex]Area = \frac{1}{2}* 3*5.4+\frac{1}{2}* 3*5.4=8.1+8.1=16.2[/tex]
Total Area = [tex]108+27+16.2= 151.2[/tex]
Answer: 151.2 ft²
Hope that helps!
The
Stem-and-Leaf Plot shows the amount of money each student spends
on travel per day in dollars. What is the median for the data in this graph?
Stem Leaf
A) $35
B) $48
C) $53
D) $54
Answers
Using it's concept, it is found that the median for the data given in the graph is given by:
B) $48
What is the median of a data-set?The median of a data-set is the value that separates the bottom 50% from the upper 50% of values.
In this problem, the graph has 16 values, already ordered. It is an even number, hence the median is the mean of the 8th and the 9th values, which considering the key are both 48, hence the median is of $48 and option B is correct.
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Answer:
B) $48
Step-by-step explanation:
Which values of x and y would make the following expression represent a real number?
Answers
The complete question is
"Which values of x and y would make the following expression represent a real number? (4 + 5i)(x + yi)"
The value of x and y are all points that satisfy the equation would be,(4,-5).
How to find the simplify the expression?Use the distributive property to simplify the expression.
The given expression is,
(4 + 5i)(x + yi)
4(x + yi)+ 5i (x + yi)
4x + 4yi + 5xi + 5yi^2
We know that i^2 = -1
4x + 4yi + 5xi - 5y
(4x - 5y) +i ( 4y + 5x)
In x+iy, x is the real part and y is the imaginary part.
If the given expression represents a real number it means the imaginary part must be zero.
4y + 5x= 0
All the points which satisfy the above equation are the values of x and y for which the given expression is a real number.
For eg. (4,-5)
4y + 5x
4(-5) + 5(4)
= 0
LHS=RHS, which means the point satisfies the equation and the value of x and y are (4,-5).
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Answer:
x = 4, y = -5 or the 3rd option
Step-by-step explanation:
just took the test
Combine the radicals 9√x-3√x-
06
O 6√x
O-6√2x
0-6
Answers
Answer:
6√x
Step-by-step explanation:
9√x - 3√x = 6√x
The owner of a local restaurant surveyed her staff on their preference of uniform color. The results are displayed in the table below. Which pair of samples is most representative of the preference of all the staff?
Answers
Answer:
my bro you gotta put the table down
Step-by-step explanation:
A rod is cut into 8 equal pieces.what fraction of the rod does 1 piece represent
Answers
Answer:
1/8
Step-by-step explanation:
you divide 1 by 8 which is 1/8.
proportional relationships, please help!
Answers
Answer:
y = 5/2 x
Step-by-step explanation:
y varies directly with x meaning this equation : y=kx
you plug in the information given
10 = k(4) and then solve ... k = 10/4 which simplifies to 5/2
Can I get some help please
Answers
The answer is C , because the ends of the line are going from negative infinity to positive infinity
Does anybody know the answer to this
Answers
substitute 3 in X's place
-2x + 5 = -2(3) + 5 = -6 + 5 = -1
hope it helps...!!!
So it’ll look like this:
F(3)= -2(3) + 5
Then you’ll solve which would be:
F(3)= -6 + 5
Answer is -1
The volume of a cylinder is 63pi cm cubed. If the radius is 3 cm, what is the height of the cylinder?
Answers
Answer:
height of a cylinder = V/ πr2. = 5.002 units.
Step-by-step explanation:
correct me if i wrong
WS
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Question 16(Multiple Choice Worth 1 points)
(02.03 LC)
Triangle ABC is transformed to triangle A' B' C', as shown below:
B
C
-2-10
1 2 3 4
-2
3
Which equation shows the correct relationship between the measures of the angles of the two triangles?
2
Answers
Answer:
What is this supposed to mean even?
Step-by-step explanation:
The Student Council at High School A held a Student Body President election. There are 940 students in enrolled and 625 students voted for a Student Body President. Approximately what percentage of the student body voted for Student Body President?
Answers
Answer:
65 %
Step-by-step explanation:
625 out of 940 is what % ?
625/940 x 100% = 66.49%
A boat is 100 m from the bottom of a 75 m high cliff. Determine the angle of elevation
from the boat to the top of the cliff. (Round to the nearest degree.)
Answers
Explanation: tanθ=(height/distance)
tanθ=75/100
θ=tan^-1(75/100)
θ=36.87≈37
Which lists all of the x-intercepts of the graphed
function?
O (0, 6)
O (1, 0) and (2, 0)
O (1, 0), (2, 0), and (-3, 0)
O (1, 0), (2, 0), (-3, 0), and (0, 6)
Answers
Answer:
(1, 0), (2, 0), and (-3, 0)
Step-by-step explanation:
The x intercepts are where it crosses the x axis. It crosses at (-3,0), (1,0) and (2,0)
On page 3, what do the words "breathed in deep" suggest? help me pls asap!
Answers
Answer: "It’s the kind of breath you will see a small baby take. A natural, inaudible inhalation that makes the belly rise and fall gently as you inhale and exhale. The diaphragm is the main breathing muscle"
Step-by-step explanation:
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15%
per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money
values to the nearest penny.)
O y = 18(1.15)
Oy=18(0.15)
Oy=20.7(1.15)*
Oy= 20.7(0.15)
Answers
The equation that can be used to find the value of the poster after x years is y = 18(1.15)^x.
What is the equation that can be used to find the future value of the poster?The formula for calculating future value:
FV = P (1 + r)^n
Where:
FV = Future value P = initial valueR = rate of increaseN = number of yearsy = 18(1.15)^x.
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Use the Pythagorean theorem to find the distance between the points (1,1) and (5,7).?
Answers
Check the picture below.
please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section.
Answers
The 3D prism that produced the cross-section of a triangle is a triangular prism.
How to describe the 3D prism?From the given figure, we can see that the cross-section is a triangle
One of the faces of a triangular prism is a triangle.
This means that when the triangular prism is cut vertically, a triangle face is created
Hence, the 3D prism that produced the cross-section of a triangle is a triangular prism.
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Please help! This is reflections in geometry! Thank you.
Answers
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
Reflection of coordinatesA reflected coordinates are mirror images of each other. From the given diagram, the coordinate points are;
P = (-4, -3)
Q = (-2,-4)
R = (1, -2)
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
The y coordinates are multiplied by a factor of 2
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