Logarithms
Convert between exponential and logarithmic form; evaluate logs; product, quotient, and power rules; expand and condense expressions; change of base; natural logarithm (ln).
13 worksheetsRead the explainer →
- 1Convert Between Exponential and Logarithmic FormRewrite expressions between b^x = y and log_b(y) = x forms.adaptive
- 2Evaluate Logarithms (Integer Results)Evaluate log_b(x) when the result is a whole number.adaptive
- 3Evaluate Logarithms (Fractional Results)Evaluate logarithms that produce negative or fractional results.adaptive
- 4Product Rule of LogarithmsApply log_b(mn) = log_b(m) + log_b(n) to expand or condense.adaptive
- 5Quotient Rule of LogarithmsApply log_b(m/n) = log_b(m) - log_b(n) to expand or condense.adaptive
- 6Power Rule of LogarithmsApply log_b(m^p) = p·log_b(m) to move exponents.adaptive
- 7Expand Logarithmic ExpressionsExpand a single logarithm into a sum/difference using all log rules.adaptive
- 8Condense Logarithmic ExpressionsCombine multiple logarithms into a single logarithm.adaptive
- 9Change of Base Formula and Natural LogarithmUse log_b(x) = ln(x)/ln(b) to evaluate logs on a calculator; interpret ln.adaptive
- 10The Richter ScaleCompare earthquake energies on the logarithmic Richter scale.easy
- 11The pH ScaleCalculate pH values on the logarithmic pH scale.medium
- 12The Decibel ScaleCompare sound intensities on the logarithmic decibel scale.medium
- 13Reading Logarithmic ScalesInterpret movement along a base-10 logarithmic scale.hard