Practice Logarithm Properties in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The three fundamental rules of logarithms: the product rule , the quotient rule , and the power rule .
Logarithms were invented to turn hard operations into easy ones. Multiplication becomes addition, division becomes subtraction, and exponentiation becomes multiplication. This is why slide rules worked—they added lengths (logarithms) to multiply numbers.
Showing a random 20 of 50 problems.
Example 1
easyUse the product rule to expand .
Example 2
mediumGiven , find .
Example 3
mediumExpand .
Example 4
challengeProve that follows from the product rule for integer .
Example 5
easyEvaluate .
Example 6
easyUse the quotient rule to expand .
Example 7
easyCondense into a single logarithm.
Example 8
hardExpress in terms of natural logarithms.
Example 9
easyUse the quotient rule to write as a difference.
Example 10
mediumGiven and , find .
Example 11
mediumCondense into a single log.
Example 12
mediumExpand fully.
Example 13
mediumGiven and , find .
Example 14
easyCondense into a single logarithm.
Example 15
mediumSolve for .
Example 16
mediumGiven and , find .
Example 17
easyUse the power rule to rewrite .
Example 18
mediumRewrite in exponential form.
Example 19
mediumExpress in expanded form.
Example 20
easyUse the power rule to rewrite .