2²ˣ = 6ˣ⁻³
How would I convert this to logarithmic form, then solve in log M / log N format?

Answers

Answer 1

6 = 2 • 3, so

6ˣ⁻³ = 2ˣ⁻³ • 3ˣ⁻³

Then in

2²ˣ = 6ˣ⁻³

we would have

2²ˣ = 2ˣ⁻³ • 3ˣ⁻³

2²ˣ / 2ˣ⁻³ = 3ˣ⁻³

2²ˣ⁻ˣ⁺³ = 3ˣ⁻³

2ˣ⁺³ = 3ˣ⁻³

Now take the logarithm of both sides. The base you choose doesn't matter.

log(2ˣ⁺³) = log(3ˣ⁻³)

Recall that log(aⁿ) = n log(a), so that the equation reduces to

(x + 3) log(2) = (x - 3) log(3)

Solve for x :

log(2) x + 3 log(2) = log(3) x - 3 log(3)

(log(2) - log(3)) x = - 3 log(2) - 3 log(3)

Recall that log(a) - log(b) = log(a/b), and log(a) + log(b) = log(ab), so that

log(2) - log(3) = log(2/3)

- 3 log(2) - 3 log(3) = - 3 (log(2) + log(3)) = - 3 log(6)

So, we get

log(2/3) x = - 3 log(6)

x = -3 log(6) / log(2/3)

As I mentioned, the base of the logarithm doesn't matter, x will always have the same value of about 13.257.


Related Questions

M<A=45
A. straight
B. obtuve
C. right
D. acute​

Answers

Answer:

d. acute

Step-by-step explanation:

acute angles are anything less than 90 degrees :)

Acute is anything less than 90°

A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?

8.8 pounds
12.7 pounds
61.6 pounds
89.1 pounds

Answers

Answer:

8.8 pounds

Step-by-step explanation:

28 kg/7 days =4 kg per day

2.2 pounds * 4 kg = 8.8 pounds

Answer:

A 8.8 pounds

Step-by-step explanation:

how many sig figs does 5 280 feet have ?

Answers

It has 3 sig figs because 0 is not significant in this case because it’s at the end

Answer:I think 3

Step-by-step explanation: All numbers not zero, so 5 2 8

ME ajudem porfavor não aguento mais, tá muito dificil


questão: Determine o valor de x em...

Answers

Answer:

say it in English plZz

I can't understand Spanish or whatever ur saying sorry

A.) Translation
B.) Rotation
C.) Reflection
D.) Dilation

Answers

Answer: Dilation

Step-by-step explanation: Dilations are when a shape is transformed into something bigger or smaller

Chick-fil-A offers its customers a choice of regular and diet soda. Last night, Chick-fil-A served 50 sodas in all, 27 of which were regular. What percentage of the sodas were regular?

Answers

Answer:

54%

Step-by-step explanation:

We know Chick-fil-A served 50 sodas in all, 27 of which were regular. The fractional form of this is 27/50. Now, we can convert this to a fraction with a denominator with 100, then a percentage. 27/50 is equal to 54/100.

54/100 is 54%

Answer:

is 54.the max is 100 percent.the percentage of regular sodas is 54 percent.you do this by timing 50 and 27 by 2 to get 100 and 54.

Step-by-step explanation:

Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept form. ​(​-6,6), (6,2)

Answers

Point-Slope form = y-y1=m(x-x1)

Y-6 = -1/3 (x+6)

Slope-intercept form = Y=mx+b

y = -1/3 + 4

The equation of line is y= -2/3x + 2.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points: (​-6,6), (6,2)

Slope= (-2 - 6)/( 6 -(-6))

slope= -8 / 12

slope= -2/3

Now, using slope intercept form

y-b = m(x- a)

y- 6 = -2/3( x + 6)

y -6 = -2/3x - 4

y= -2/3x + 2

Hence, the equation of line is y= -2/3x + 2.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

please help me i cant do this question

Answers

Answer:

Step-by-step explanation:

[tex]x^{\frac{1}{2} }[/tex] × [tex]x^{\frac{1}{4} }[/tex] = [tex]x^{\frac{1}{2} +\frac{1}{4} }[/tex] = [tex]x^{\frac{3}{4} }[/tex]

Please answer give it too me now

Answers

Answer:

5/3

Step-by-step explanation:

HTH :)

I need help NOW please!!!

Answers

Answer:

B)34

Step-by-step explanation:

Answer:

B.34°

supplementary angles

their sum is 180

180=146+x

x=180-146=34

Eric earned 60 points on his last test. If there was 75 possible points, WHAT was his PERCENT grade?

Answers

Answer:

80

Step-by-step explanation:

Eric-- 60/75

Percentage of Eric ---- 60/75 *100

Eric got 80 percentage in his last test.

Peter​ says, "If you subtract 12 from my number and multiply the difference by −7​, the result is −175​." What is Peter​'s ​number​

Answers

Answer:

37

Step-by-step explanation:

let’s say peter’s number is x

(x-12)(-7) = -175

-7x + 84 = -175

-7x = -259

x = 259/7

x = 37

Answer:

The number is 37.

Step-by-step explanation:

-175 ÷ -7 = 25

25 + 12 = 37

You have to work backwards from -175 by doing the reverse of what peter did to get the original number.

Amy needs to fill a tank that has a capacity of 112L. She using a bucket to collect water from the tap. The bucket can hold 7L of water. How many trips she needs to make to fill half of the tank? *

Answers

Answer:

8 trips

Step-by-step explanation: divided 112 by 2 then I got 56 which I then divided that by seven which gave me the answer of 8

State the equation that results when both sides of 2x - 3y = -4 are multiplied by -3.

Answers

Answer:

6x - 9y = -12

Step-by-step explanation:

2x - 3y = -4  multiply both sides by 3 by adding paranthesis to represent this

3( 2x - 3y ) = 3 (-4)   Then use distributive property for the left side equation

6x - 9y = -12               Finally just multiply -4 by 3 and you get this equation

What is the solution of the equation p + r + 2 = 3r – 4 – 3p in terms of r?

Answers

Answer:

[tex]r=2p+3[/tex]

Step-by-step explanation:

Please help will give brainlist

Answers

Answer:

g(10) = 31

f(-3) = -2

h(2) = -7

j(7) = 333

j(3) = 17

I hope the last 2 were for the same function lol

(2 x 1058) * (2 x 10-27)

Answers

2*1058=2116
27-10*2=34
2116*34=71944
I’m guessing that X is a times sign

A bowl of fruit contains a 4: 1 ratio of blueberries to strawberries. There is a total of 65 berries in the bowl. How many of them are blueberries and how many are strawberries?

Answers

9514 1404 393

Answer:

52 blueberries13 strawberries

Step-by-step explanation:

There are a total of 4+1 = 5 ratio units, so each one stands for 65/5 = 13 berries.

  blueberries : strawberries = 4 : 1 = 52 : 13

There are 52 blueberries and 13 strawberries in the bowl.

A recipe calls for 2/3 of cups of milk for 11 cookies. How many cups of milk are needed to make 165 cookies?

Answers

Answer:

10 cups of milk

Step-by-step explanation:

Make a proportion, where x is the number of cups of milk for 165 cookies:

[tex]\frac{2/3}{11}[/tex] = [tex]\frac{x}{165}[/tex]

Cross multiply and solve for x:

11x = 110

x = 10

So, 10 cups of milk are needed to make 165 cookies

10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value)

Answers

Answer:

r = 50000

P (r) = 0.7r - 35000

Step-by-step explanation:

Given cost function is

C (r) = 0.85r + 35000

and revenue function is

R (r) = 1.55r

At break even point, revenue is equal to cost

R(x)= C(x)

1.55r = 0.85r+35000

Subtract 0.85 from both sides

0.7r = 35000

divide by 0.7 on both sides

r = 50000

Profit function

P(x)= R(x)- C(x)

P(r) = 1.55r - (0.85r+35000)

P(r) = 1.55r - 0.85r - 35000

P(r) = 0.7r - 35000

(2x+5+8)/x-2 there should be a remainder left, pls help

Answers

Answer: 13/2

Decimal answer 6.5

im sorry if it was wrong it was what I got

Step-by-step explanation:

The directions on a sewing pattern say to buy an extra 12.5% of fabric to account for error. Sam needs 2.75 yards of fabric to make a shirt, so he buys 2.4 yards. Choose the correct statement.

A.Sam bought the correct amount of fabric because he bought what was suggested.

B.Sam bought the correct amount of fabric because he needs less than 2.4 yards.

C.Sam did not buy the correct amount of fabric because he needs less than 2.4 yards.

D.Sam did not buy the correct amount of fabric because he should have bought 3.09 yards​

Answers

Answer:

Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Step-by-step explanation:

Total fabric needed by Sam = 2.75

According to directions on a sewing pattern they say to buy an extra 12.5%

So, extra fabric would be: 12.5% of 2.75

Solving

[tex]12.5\% \ of \ 2.75\\=\frac{12.5}{100}\times 2.75 \\=0.343[/tex]

Now adding 0.343 into 2.75 to get extra fabric quantity:

2.75+0.343

=3.09

Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

What is the simplified value of the expression below?

Negative 2.6 + 5.8
–8.4
–3.2
3.2
8.4

Answers

Answer:

i did that quiz the answer is 3.2

Step-by-step explanation:

your welcome

Answer:

3.2

Step-by-step explanation:

Clare knows that Priya has a bunch of nickels and dimes in her pocket and that the total amount is $1.25. Find one possibility for the number of nickels and number of dimes that could be in Priya's pocket. Write an equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket. Explain what the point (13,6) means in this situation. Is the point (13,6) a solution to the equation you wrote? Explain your reasoning.

Answers

Answer:5x + 10y = 125

Step-by-step explanation

Number of nickel = x

Number of dime = y

Nickel = 5 cent

Dime = 10 cent

Total value = $1.25

Total value should be converted to cent since both dime and nickel are both in cent

= $1.25 * 100 = 125 cents

Therefore,

5x + 10y = 125 cents

what is the difference between twice a number that is 5 more than it is 3
NEED THIS IN NUMBER FORM

Answers

Answer:

The difference between twice a number and a number that is 5 more than 3. Write an equation that could be used to find the value of the number n,

Answer:

2n-8

Step-by-step explanation:

twice a number = 2n

5 more than 3 is 8

difference means subtraction

3(2x − 5) = 6x + k , whats the value of k?

Answers

Answer:

k=-15

Step-by-step explanation:

3(2x-5)=6x+k

open the bracket by multiplying the contents of the bracket by +3

6x-15=6x+k

collect.like.terms(C.L.T)

6x-6x-k=+15

-k=+15 or

-k=15

switch the signs equal to sign(=)

k=-15

3/5n+15=10+2/5n what is n

Answers

[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{3}{5}n +15=10+\dfrac{2}{5}n}[/tex]

[tex]\mathsf{\bf{SUBTRACT}\ \mathsf{by\ \dfrac{2}{5}n\ from\ both\ of\ your\ sides}}[/tex]

[tex]\mathsf{Like: \dfrac{3}{5}n+15-\dfrac{2}{5}n=\dfrac{2}{5}n+10-\dfrac{2}{5}n}[/tex]

[tex]\mathsf{\bf{CANCEL: \dfrac{3}{5}+\dfrac{2}{5}}}\textsf{out\ because that gives you\ 1}[/tex]

[tex]\textsf{Solve\ the set we have left over}[/tex]

[tex]\mathsf{Our\ new\ equation\ becomes: \dfrac{1}{5}n+15=10}[/tex]

[tex]\mathsf{\bf{SUBTRACT}}\textsf{ by 15 on both of your sides}[/tex]

[tex]\mathsf{\dfrac{1}{5}n+15-15=10-15}[/tex]

[tex]\mathsf{Cancel\ out: 15-15\ because\ that\gives\ you\ 0 }[/tex]

[tex]\mathsf{Keep: 10-15\ because\ it\ helps\ us\ solve\ for\ your\ n }[/tex]

[tex]\mathsf{10-15=-5}[/tex]

[tex]\mathsf{New\ equation: \dfrac{1}{5}n=-5}[/tex]

[tex]\mathsf{\bf{MULTIPLY}\mathsf{\ both\ sides\ by\ 5}}[/tex]

[tex]\mathsf{\dfrac{1}{5}n\times5=5\times-5}[/tex]

[tex]\mathsf{Cancel\ out\ \dfrac{1}{5}\times5 \ because \ it \ gives \ us \ 1}[/tex][tex]\mathsf{Keep: 5\times -5\ because\ it\gives\ us\ the\ value\ of\ your\ n}[/tex]

[tex]\mathsf{n =5\times-5}\\\mathsf{5\times-5 = -25}[/tex]

[tex]\textsf{Thus, \underline{\bf{n = -25}}}\checkmark[/tex]

[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: \boxed{\boxed{\bf{n =-25}}}}}}\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Consider the two graphs above.

Which statement best describes the graphs?

A. Graph 1 represents a proportional relationship, but graph 2 does not.

B. Graph 2 represents a proportional relationship, but graph 1 does not.

C. Both graph 1 and graph 2 represent proportional relationships.

D. Neither graph 1 nor graph 2 represent a proportional relationship.

Answers

Answer:

B. Graph 2 represents a proportional relationship, but graph 1 does not.

Step-by-step explanation:

All proportional relationships pass through the origin. Graph 2 does but Graph 1 does not. Additionaly, Graph 2 is a straight line that represents a proportional relationship. Another way to find out if it is proportional is to find the constant of proportionality by dividing the y by the x in different parts of the line. The numbers should all have the same constant of proportionality.

Examples (all found in Graph 2):

15/3 = 5

10/2 = 5

5/1 = 5

B, Graph 2 represents a proportional relationship, but graph 1 does not

Sorry if I’m work



I hope this helps

What is the value of the expression when a = –5 and c = –1

Answers

Answer:

1 times anything is always the number that is being multiplied so the answer would be 5

Step-by-step explanation:

Ali was earning $15 per hour before receiving a 10% raise. What is Ali’s new hourly rate? Write and solve an equation.

Answers

Answer:

12.56

Step-by-step explanation:

A was earning $15 per hour before receiving a 10% raise. What is Ali’s new hourly rate? Write and solve an equation.

12.60 is the correct answer rounded up
Other Questions
A cyclist rode for 3.5 hours and completed a distance of 60.9 miles. If she kept the same average speed for each hour, how far did she ride in 1 hour? Part A Estimate the quotient. Include an equation to show your work. Explain your thinking.? Part B Find the exact distance she rode in 1 hour by completing the division. PLEASE HELP! PLS HELP 25 Points!! What number, rounded to the nearest hundred thousandth (five decimal places), is represented by e?Enter your answer as a decimal, like this: 42.53647 Identify an element that is NOT in its standard state.Choose the one alternative that best completes the statement or answers the question.A) N2(g)B) Xe(g)C) Ca(s)D) N(g) Kyrstin dice: Son las diez de la maana. * How can I negate this sentence? For any whole number b that is a PERFECT SQUARE The movement to end slavery was led by white people in the Northern states.TrueFalse Which of the shows the correct sums that would be found when clustering is used to find the answer to the problem 41 x 22?820 + 82 = 912800 + 2 = 802820 + 82 = 902820 + 80 = 900 What was one effect of the American Revolution on the women of North Carolina?They gained independence from Britain with the male colonists.They gained greater representation in the colonial government.They became able to own land and property in larger numbers.They served in and assisted Patriot militias in sizable numbers. Find the value of the function below for the given x-valueF{x} = -5x-1 when x=-3 Help please ill give brainliest !!! Which of the following issues is causing pollution and damage to water ecosystems in Nigeria?A.dam construction on the Niger RiverB.toxic dumping by factoriesC.spills from the nations oil productionD.too many older vehicles on the roads Remove the brackets and simplfy 5-(6a -3b -8) f(x) = |3x+5| + 6g(x) =7 find (f+g) (x) Which phrase best describes what the image is targeting? how one may feel ashamed about oneselfhow one does not really care about appearancehow one may feel about consuming food in excess how one may feel about exercising too little during the week African Americans seeking free land in the Midwest facedO A. a waiting period before land ownership,O B. competition by whites.O c. discrimination by whites.O D. all of the above Who of the following were dictators of Cuba? What are the other properties of pure substance Which statement best synthesizes information from both sources?A. Diners who want to try something weird and different should visit Chuck's.B. Diners who want to eat healthy vegetarian cuisine should avoid Chuck's. C. Diners who want to eat good-tasting food should avoid Chuck's. D. Diners who want a pleasant surprise should visit Chuck's. Why were conquests of North America less successful than conquests of South America What is the correlation of the scatter plot pictured below?Question 8 options:-.911-.420.002.798