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

1 Answer
Jan 1, 2016

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