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Solving a Logarithmic Equation  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel 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 x3 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 x3 is equal to 4 squared, 4 squared is 16, x3=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, 193 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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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Sample Problems (6)
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Solving a Logarithmic Equation
Problem 1 10,149 viewsSolve:
log_{3}(x² + 10x + 25) = 4 
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Problem 2 8,579 viewsSolve:
2log_{4}(3x − 2) = 6 
Solving a Logarithmic Equation
Problem 3 7,782 viewsSolve:
log_{7}(5 − x) = log_{7}8 
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Problem 4 2,035 views 
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Problem 5 1,967 views 
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Problem 6 1,845 views
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