# If #5^x = 3#, what does #5^-(2x)# equal?

##### 1 Answer

Jun 28, 2017

#### Explanation:

**1. First, take the log (base 10) of both sides.**

**2. When you have an exponent** inside of a log, you can take that exponent out and multiply it by the rest of the log.

This is known as the **power rule** of logarithms.

**3. Now divide both sides by #log(5)# to find #x#.**

**4. Now, plug #x# (in terms of the logs) into the second expression.**

Let's evaluate the power first. (I used a calculator here.)

So

Hope this helps! :)