Logarithm Laws Practice: Expand, Condense, and Evaluate

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Designed for 11th grade math students. Simplify each expression using the product, quotient, power, or change-of-base rules.

Expand log_5(x * y * z)
Expand log_2(a^4)
Expand log_3(x / 9)
Condense into a single logarithm: log_4(12) - log_4(3)
Condense into a single logarithm: 2 * log_b(x) + 3 * log_b(y)
Condense into a single logarithm: log_10(x) - 4 * log_10(y) - log_10(z)
Use the change-of-base formula to rewrite log_7(50) using common logs (base 10).
True or False: log_2(x + 8) = log_2(x) + 3

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Logarithm Laws Practice: Expand, Condense, and Evaluate

Answer key

Expand log_5(x * y * z)
log_5(x) + log_5(y) + log_5(z)
Expand log_2(a^4)
4 * log_2(a)
Expand log_3(x / 9)
log_3(x) - 2 (since log_3(9) = 2)
Condense into a single logarithm: log_4(12) - log_4(3)
1 (since log_4(12 / 3) = log_4(4) = 1)
Condense into a single logarithm: 2 * log_b(x) + 3 * log_b(y)
log_b(x^2 * y^3)
Condense into a single logarithm: log_10(x) - 4 * log_10(y) - log_10(z)
log_10(x / (y^4 * z))
Use the change-of-base formula to rewrite log_7(50) using common logs (base 10).
log(50) / log(7)
True or False: log_2(x + 8) = log_2(x) + 3
False. Logarithms do not distribute over addition.