Solving for X in a complex log problem  TOPIC_SOLVED

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Solving for X in a complex log problem

Postby burnbird16 on Sat May 22, 2010 1:41 am

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!
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  TOPIC_SOLVED

Postby stapel_eliz on Sat May 22, 2010 12:34 pm

burnbird16 wrote: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. :wink:
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