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