Question

What's the inverse of y=a^x

Answer 1

\[\large \color{red}y=a^\color{red}x\]switch x and y.

Answer 2

And then tell me what you get.

Answer 3

then resolve for y

Answer 4

Are you able to write your equation once you switch the variable, @minisweet4 ?

Answer 5

x=a^y then would I have to square root something

Answer 6

Not exactly.

Answer 7

to undo a base to an exponent you log it

Answer 8

because we see y is a power, we can use log rules to bring that power down. take the natural log of both sides,

Answer 9

And write down what you have once you do that.

Answer 10

I honestly don't know how to do the next part

Answer 11

multiply \(\ln\) to both sides, and write it down :)

Answer 12

Then we will move on to the next step.

Answer 13

I would not say "multiply" ln(x) is a function..so we need to take ln of both sides, but to know what ln is you must know what \(y=a^b\iff \log_a(y)=b\)

Answer 14

its sort of built into the definition...

Answer 15

Do NOT "multiply ln". That does not mean anything. "ln" is NOT a factor. It is a function.

You have \(y=a^{x}\)
Introduce the logarithm: \(ln(y)=ln\left(a^{x}\right)\) -- No multiplication going on, there.

Answer 16

She wasn't taking the natural log of both sides, so instead to visualize i said "multiply" eh