Question

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

y=1/3x

y=log3x

y=(1/3)x

y=log1/3x

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

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* \log a`

Applying the same,

`\Rightarrow \log x=y* \log 3`

`\Rightarrow y=(\log x)/(\log 3)`

As,

`\log_b a=(\log a)/(\log b)`

Applying the same,

`\Rightarrow y=\log_3 x`

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