Solving Logarithmic Equations and Inequalities
Method

Solving Logarithmic Equations Algebraically

If only one side of a logarithmic equation can be written as a single logarithm with base with and then the equation can be solved by using the definition of a logarithm.
Since logarithms are defined only for positive numbers, must be a positive number. Consider an example equation.
To solve this equation, four steps must be followed.
1
Isolate the Logarithmic Expression on One Side
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The first step is to isolate the logarithmic expression. This can be done by using inverse operations.
2
Use the Definition of a Logarithm
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Once the logarithmic expression is isolated, the definition of a logarithm can be used to eliminate the logarithm.
3
Solve the Obtained Equation
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The obtained equation can now be solved.
Solve for
4
Check the Solutions
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Finally, to detect any extraneous solutions, the obtained value can be checked by substituting it into the original equation.
Evaluate left-hand side

A true statement was obtained, so the solution is not extraneous.
Exercises