Practice Change of Base Formula in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A formula for converting a logarithm from one base to another: .
Your calculator only has and buttons. The change-of-base formula lets you compute ANY logarithm using whichever base you have available. It works because all logarithms are proportional to each other—changing base just changes the scale factor.
Showing a random 20 of 50 problems.
Example 1
easyEvaluate without a calculator.
Example 2
challengeIf , express and in terms of .
Example 3
hardIf , express in terms of .
Example 4
mediumSolve for .
Example 5
mediumEvaluate exactly.
Example 6
easyEvaluate .
Example 7
hardProve that using the change of base formula.
Example 8
mediumSimplify to an exact fraction.
Example 9
mediumShow that using change-of-base.
Example 10
easyRewrite as a ratio of common (base-10) logarithms.
Example 11
easyEvaluate for any base , .
Example 12
mediumSimplify to an exact fraction.
Example 13
easyUse change-of-base to write in terms of base 2 logs.
Example 14
hardSolve for .
Example 15
mediumEvaluate exactly.
Example 16
hardIf and , find in terms of and .
Example 17
easyEvaluate by recognizing a power.
Example 18
challengeSolve for .
Example 19
mediumEvaluate exactly.
Example 20
easyRewrite as a ratio of natural logs.