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Solving a Logarithmic Equation with Multiple Logs - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

When given a problem on solving a logarithmic equation with multiple logs, students should understand how to condense logarithms. By condensing the logarithms, we can create an equation with only one log, and can use methods of exponentiation for solving a logarithmic equation with multiple logs. This requires knowledge of the product, quotient and power rules of logarithms.

Solving a logarithm equation where we have more than one log on either side, so really when we're solving a logarithm equation where we have two or more logs on either side, what we need to do is combine them to make sure we just get one log on a single side okay? So how we do that is using our properties of logs, remember if we are adding we can throw this together to be multiplication, if we're dividing we can throw them together to be division okay? Once we use all those properties of logarithms and we have a single log on one side and either a single log or a number on the other we can just solve them as we do what I will call simple log equations put in exponential form or know that the insides of logarithms have to be the same.

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