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Gnesinka [82]
3 years ago
11

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

Mathematics
2 answers:
marissa [1.9K]3 years ago
6 0

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)}

Tomtit [17]3 years ago
4 0

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 <em>function</em>, we have to rewrite this equation by isolating y. We do this with logarithms:

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

Hence the answer.

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