Question

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

Answer 1

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

Explanation:

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)`

Further reading:
Wikipedia Definition
Logarithmic Rules