# How do you solve #log_12 (p^2-5p)=log_12 (8+2p)#?

##### 2 Answers

Hi there! To solve this, you must recognize that if you have logs of the same base, you can drop them, leaving you with the functions inside.

#### Explanation:

When you have:

Since both logs in your question have a base of 12, you can drop them, leaving you with:

Rearranging we get:

Collecting like terms:

Factoring this **simple trinomial** (finding numbers that multiply to -8 and add to -7):

Solving each piece we get:

And that's it, those are the p values that would make those expressions equal. Hopefully everything was clear and helpful! If you have any questions, please feel free to ask! :)

#### Explanation:

Both the logarithms have the same base 12.

So,

The roots of this quadratic equation are

Both the roots are admissible for both the logarithms..