Practice Solving Logarithmic Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Solving equations containing logarithms by converting to exponential form or using log properties to combine and simplify.
If logarithms trap the variable inside a \log, converting to exponential form releases it. The key insight is that \log_b(\text{stuff}) = c means b^c = \text{stuff}—just rewrite and solve.
Example 1
easySolve \log_2(x) = 5.
Example 2
mediumSolve \log(x+3) + \log(x-1) = \log(5).
Example 3
mediumSolve \ln(x^2 - 4) = \ln(3x).
Example 4
hardSolve \log_3(x+6) - \log_3(x-2) = 2.