Question

How do you find the inverse of logarithmic functions?
Ex:h(x) = log7 x
Ex:f(x) = 3^x - 1
Ex:h(x) = e^2x
Ex:f (x) = 6x

Answer 1

rewrite in equivalent exponential form
\[\log_7(x)=y\iff 7^y=x\]

Answer 2

What satellite73 said, which basically is that you raise the base by the logarithm of the same base.

Answer 3

So is it the same for all of those?

Answer 4

Ex:h(x) = log7 x THIS IS THE ONLY LOGARITHMIC FUNCTION YOU LISTED.
Ex:f(x) = 3^x - 1 THIS IS AN EXPONENTIAL FUNCTION.
Ex:h(x) = e^2x THIS IS AN EXPONENTIAL FUNCTION.
Ex:f (x) = 6x THIS IS A LINEAR FUNCTION.

So, it is the same for all LOGARITHMIC functions.

Answer 5

The other ones said that the answer was logarithmic

Answer 6

If a function is exponential, you need to take the logarithm of both sides to get the answer of x (as a a logarithmic function).

Answer 7

It says
Write the inverse of g(x) = e^x

g^-1(x) = _____.

a)log e x
b)log x e
c)log e y
so how would you do that?

Answer 8

log_e(x) = ln(x)

g^(-1) (x) = ln(e^x)
g^(-1) (x) = x

Since ln(x) = log_e(x) the logic is "e raised to what equals e^x? The answer is x."

Answer 9

Oops.

Answer 10

what?

Answer 11

You switch the x and y and then you solve for y and that's the inverse.

Answer 12

You solve for y using what satellite73 said on the first post.

Answer 13

where y = f(x) or h(x) or whatever.

Answer 14

Here: https://www.youtube.com/watch?v=btmXzOSn1tY

Answer 15

Okay thank you that's a lot of help. This stuff really confuses me

Answer 16

No problem.