How do you find the inverse of #y = 3^x#?

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Answer 1 · 2016-01-01T22:54:45

The inverse of #y=3^x# is #x=log_3(y)#.

Let's consider the template equation #y=a^b#.

Stating the apparent: If you know #a# and #b#, then you can calculate #y# by using exponentiation.

When you have the variables #y# and #b#, you use roots to calculate #a#, such as #root(3)27#.

But what if you have the variables #y# and #a#, and you must calculate the exponent #b#? This is the case where logarithms are used.

If you need to calculate how many times some number #a# is multiplied by itself to produce #y#, you use logarithms.

Too long; Didn't read:
In the case of #y=3^x#, the inverse of exponentiation uses a logarithm of base #3#, which is the answer sought:

#x = log_3(y)#