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Solving Simple Logarithmic Equations - Concept 26,759 views

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!

In order to understand solving logarithmic equations, students must understand the basics of logarithms, and how to use exponentiation to access the terms inside the logarithm. Some more complicated instances of solving simple logarithmic equations require knowledge of the product, quotient and power rules of logarithms in order to simplify complex terms.

Solving simple logarithm equations and what I mean by simple logarithm equations is basically logarithm equation that is in logarithm form. so basically you have a log, a base, your term and then an answer. So basically, 3 things, I'll call this a simple logarithmic equation.
Really all you have to do whenever you're solving something in this form is put into exponential form, okay? No matter what the x is we're going to deal with x's in all 3 of these spots. Just put into exponential form and solve, okay? So this one the 3 is going to come up and around leaving us with x=3 to the -2 and this problem has now just turned into evaluating an exponent. The negative puts everything in the bottom, the 2 squares it and we end up with x=1 over 9.
So whenever we ha- any time we have an equation in logarithm form, in order to solve it put an exponential and then solve it as you would in the other exponential equations.