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Solving a Logarithmic Equation - 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!

Just as we can use logarithms to access exponents in exponential equations, we can use exponentiation to access the insides of a logarithm. Solving logarithmic equations often involves exponentiating logarithms in order to get rid of the log and access its insides. Sometimes we can use the product rule, the quotient rule, or the power rule of logarithms to help us with solving logarithmic equations.

Solving simple logarithm equations and what I mean by simple logarithm equations is actually ones that we have a single log and one or both sides so we only have a maximum of two logs one on the right one on the left and basically what what we do in these situations is put the equation into exponential form and then solve it up. The one thing we really have to be careful about is our domain and remember that we can't take the log of a negative number so whenever we get an answer we always have to check.
Okay so behind me I have a pretty straight forward example log base 4 of x-3 is equal to 2 okay? To solve this out all we want to do is put this into exponential form so we bring the 4 up and around leaving us with x-3 is equal to 4 squared, 4 squared is 16, x-3=16 add 3 to both sides leaving us with x=19 okay? Now the last thing we have to do is check make sure this actually can go into our equation, we plug 19 in, 19-3 is 16 log base 4 of 16 is in fact 2 okay? so whenever we're solving a logarithm equation, we're only having one or two logs just put an exponential form and solve.

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