3^x : write in terms of base e and simplify! ...?

Answers

Answer 1

Answer: The given function is exponential. Meanwhile $<b>change of base</b>$ has something to do with logarithms. So we convert the function to logarithm function, change to the required base and convert back to exponential function.

Let

$y = {3}^(x)$

Writing the above exponential equation as a logarithmic equation, we obtain;

$log_(3)(y) = x$

We can apply the change of base formula to obtain,

$( log_(e)(y) )/( log_(e)(3) ) = x$

Or

$( ln(y) )/(ln(3) ) = x$

We can cross multiply to obtain;

$ln(y) = x ln(3)$

Taking logarithm of both sides to base e, we obtain;

${e}^( ln(y) ) = {e}^(x ln(3) )$

This implies that,

$y= {e}^(x ln(3) )$
But we know that,
$y = {3}^(x)$
Hence
${3}^(x) = {e}^(x ln(3))$

Answer 2

Answer: 3^x : write in terms of base e would

3x=e^ln3^x

=e^xln3

Related Questions

adela rode her bicycle 18.3 miles in 5 hours. which gives the best estamate of how far adela rode in 1 hour
Given this equation, what is the largest possible value for z?
3. If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
Find three consecutive even integers whose sum is 36.
Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now has $237.a. Write an equation that can be used to find the number of swimming lessons that she paid for.b. How many swimming lessons did she pay for?c. At the time she has $237, the cost of a lesson rose to $19. How many lessons can she pay for with her remaining $237?

The diameter of a circle is 130 inches. The circle has two chords of length 66 inches. What is the distance from each chord to the center of the circle?

Answers

Answer: 56

Step-by-step explanation:

The scatter plot shows the ages of children and how many stuffed animals they own.What is the range of ages for the cluster?

Answers

the answer is 8 to 10 that is the range of ages for the cluster

Describe a real-life situation where you would have a remainder?GIVE YOU 10000 POINTS!!!!!!!!!!!

Answers

At my favorite drugstore, comic books used to cost 10¢ .
(It wasn't yesterday, or even last week. In fact, the drugstore
was burned to the ground during the riots in 1964, and never
rebuilt. But I digress.)

Normally, my parents only let me buy one comic book at a time.
But before I left for summer camp, I could empty my little piggy
and spend it ALL on comic books, all at the same time ! That
was as much fun as the whole 2 weeks at camp !

I emptied my little pig. I had 67¢ in there. I headed for the
drugstore. For the whole rest of the afternoon, I stood at the
magazine rack, carefully deciding on my selections.

How many comic books did I buy ?

What was the remainder ? (How much money did I have left ?)

when in gym when you have 7 people and you need two even teams you will have a remainder of 1

Which of the following similarity statements about the traiangles in the figure is true

Answers

the second one I hope I am correct

5. The cost of a notebook increased from $4.30 to $4.58, what is the percent increase?A 5.5%
C. 6.5%
B 6%
D. 7%

Answers

The answer is 6.5
Explanation : 1. Find out the increase number by subtracting 4.58 - 4.30 = 0.28 or 6.51%
2. Divide the increase number 0.28 by 4.30 and multiple by 100 which gives you 6.51162791 .
3. Get rid of all the numbers behind 5 and you can’t round it because 1 is too small. Which then gives you the answer 6.5 :) <3

During a certain five-year period the consumer price index decreased by 40% but during the next five-year period it increases by only 20%. which if these conditions must have existed during the second five-year period..A. Inflation
B. Conflation
C. Deflation
D. Stagnation

Answers

I’m pretty sure it’s A. Inflation

Let me know if this is correct! Hope it helps God bless:)

Answer: it is A .inflation

Other Questions

six students are sitting in chairs placed in a line. in how many different orders can the students be seated ?

A teacher wants to arrange 16 chairs in equal rows in his classroom. How can he arrange the chairs? () in 4 rows, with 20 chairs in each row () in 2 rows, with 8 chairs in each row » In Brows, with 8 chairs in each row () in 3 rows, with 5 chairs in each row My Progress Sign out

Please help me solve this proof!!!!!

Is the permeter of a pentagon five times the length of one side? why or why not