Solving for X in a complex log problem

[burnbird16]

Hello all! I just got my AP Calculus summer assignment, and on it, I found a problem that's really giving me trouble. Anyone care to help?

Here it is:

log_3 x^2 = 2log_3 4 - 4log_3 5

I hope that's clear. :3

Thank you in advance for anyone kind enough to help me!

[stapel_eliz]

log_3 x^2 = 2log_3 4 - 4log_3 5

The first step is to use a log rule to convert the subtraction of two logs on the right-hand side of the equation into one log containing a division.

Since you will then have "log₃(one thing) = log₃(another thing)", you can set (one thing) equal to (another thing) and solve the resulting quadratic equation.

Don't forget, though, that you cannot have negatives inside logarithms. Only one of the quadratic equation's solutions will be valid within the original logarithmic equation.