Question

What function is the inverse of the exponential function y = 3^x?

Answer 1

Answer:

Step-by-step explanation:

First switch the y and x values:

$x=3^y$

Take the natural log of both sides to get:

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

Separate the y value:

$y=\frac{\ln(x)}{\ln(3)}$

Answer 2

Answer:

$y=\log_{3}(x)$

Step-by-step explanation:

To take the inverse of a function, swap x with y and vice versa. Therefore, the inverse of y = 3^x is x = 3^y. However, because we are being asked for a function, we have to rewrite this equation by isolating y. We do this with logarithms:

$x=3^y\\y = \log_{3}x$

Hence the answer.