Logarithms

Logarithms are the inverse of exponential functions, answering the question "to what power must a base be raised to produce a given number?" This topic covers evaluating logarithms, applying log properties to simplify expressions, solving logarithmic equations, and using the change of base formula.

Logarithmic scales appear in measuring earthquakes (Richter scale), sound intensity (decibels), and pH in chemistry. They are also fundamental to algorithm analysis in computer science.

Practice Tips

• 1Memorize the three core properties: log(ab) = log a + log b, log(a/b) = log a - log b, and log(a^n) = n log a.
• 2When solving logarithmic equations, consolidate all log terms to one side and convert to exponential form to isolate the variable.
• 3Use the change of base formula log_b(x) = ln(x)/ln(b) to evaluate logarithms with unusual bases on a calculator.