Logarithms Practice Test

About This Logarithms Practice Test

This test reviews the meaning of a logarithm before moving into more advanced equation solving. A logarithm is interpreted as an exponent, and each item connects logarithmic notation with exponential notation, function properties, or a practical model.

The set includes exact evaluation, negative logarithm values, common and natural logs, domains, vertical asymptotes, inverse functions, increasing and decreasing behavior, change of base, and pH.

Skills Covered

You will evaluate logs from known powers, rewrite between logarithmic and exponential forms, identify valid arguments and bases, describe graph features, estimate values between integers, and use logarithms in an application.

Key Facts to Remember

1. log_ba = c means b^c = a.
2. A real logarithm requires a positive argument, a positive base, and a base not equal to 1.
3. The domain of a basic log is positive real numbers, while its range is all real numbers.
4. Bases greater than 1 give increasing functions; bases between 0 and 1 give decreasing functions.

Common Mistakes to Avoid

Do not return the argument when the question asks for the exponent, include a zero endpoint in a domain, write a vertical asymptote as y = constant, or treat a logarithm base between 0 and 1 as increasing.

Practice Format

The test provides immediate feedback, worked reasoning, and a review of each incorrect option. It can be repeated freely for Algebra 2, precalculus, and exam preparation.