Question

Which of the following is the inverse of y=3x?

Answer 1

So if x is the exponent, 3 is the base, and y is the argument then this is an exponential function meaning the inverse is a logarithm so the answer can't be A or C. All you have to do is match the base, exponent, and argument into the setup for a logarithmic equation which is x=logby. Your answer should be x=log3y which looks similar to answer B.

Answer 2

Answer-

The inverse of $y=3^x$ is

$\boxed{\boxed{y=\log_3 x}}$

Solution-

The given function is,

$y=3^x$

We can get the inverse by interchanging he variable x and y among themselves and then separating each variables.

So in the inverse would be,

$\Rightarrow x=3^y$

Taking log of both sides,

$\Rightarrow \log x=\log 3^y$

As,

$\log a^b=b\times \log a$

Applying the same,

$\Rightarrow \log x=y\times \log 3$

$\Rightarrow y=\dfrac{\log x}{\log 3}$

As,

$\log_b a=\dfrac{\log a}{\log b}$

Applying the same,

$\Rightarrow y=\log_3 x$

Therefore, the inverse of $y=3^x$ is $y=\log_3 x$.