Logarithmic Equations Practice Test
20 logarithmic equations with domain checks, exact answers, and worked explanations.
Solve logarithmic equations and reject values that violate argument or base restrictions.
20 logarithmic equations with domain checks, exact answers, and worked explanations.
This test focuses on solving equations in which the variable appears inside a logarithm, inside several logarithms, or as the logarithm base. The questions progress from direct exponential conversion to equations that require combining logs and solving a quadratic.
Because logarithmic expressions have strict domains, every algebraic candidate must be checked against positive-argument and valid-base conditions.
Practice includes rewriting logarithms in exponential form, using product and quotient rules, solving common and natural logarithmic equations, handling nested logarithms, finding exact radical answers, and rejecting extraneous roots.
Do not split the logarithm of a sum, accept a zero or negative argument, allow an invalid logarithm base, omit a second algebraic root before checking it, or confuse the logarithm argument with the final value of x.
Each question provides an exact solution where possible, shows the domain check, and explains the errors represented by the other answer choices.