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loris [4]
3 years ago
6

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

Mathematics
2 answers:
tigry1 [53]3 years ago
8 0
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.
shtirl [24]3 years ago
7 0

Answer-

<em>The inverse of y=3^x is </em>

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

<u>Solution-</u>

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.

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