Grade 11 · Algebra & functions

Logarithm rules practice

Logarithm rules is a grade 11 math skill aligned to Common Core standard HSF.BF.B.5: understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 17 logarithm rules problems our math games drill.

CCSS HSF.BF.B.517 questions in the bank

Sample questions

Try 8 for free

Question 1easy

Simplify: $\log_{5}(25)$ .

$5^{2} = 25$ , so $\log_{5}(25) = 2$ .

Question 2easy

Which rule combines $\log a + \log b$ into a single logarithm?

$\log a + \log b = \log(ab)$ is the product rule.

Question 3easy

Simplify: $\log_{2}(16)$ .

$2^{4} = 16$ , so $\log_{2}(16) = 4$ .

Question 4easy

Which rule rewrites $3\log a$ as a single logarithm?

$3\log a = \log(a^{3})$ is the power rule.

Question 5easy

Simplify: $\log_{3}(9)$ .

$3^{2} = 9$ , so $\log_{3}(9) = 2$ .

Question 6easy

Simplify: $\log_{3}(27)$ .

$3^{3} = 27$ , so $\log_{3}(27) = 3$ .

Question 7easy

Simplify: $\log_{2}(32)$ .

$2^{5} = 32$ , so $\log_{2}(32) = 5$ .

Question 8easy

Simplify: $\log_{10}(1000)$ .

$10^{3} = 1000$ , so $\log_{10}(1000) = 3$ .

Tests that cover logarithm rules:

ACT PARCC PSAT/NMSQT NY State Math VTCAP

More Grade 11 skills:

Geometric sequence equations Sequences and series Function transformations Exponential and log formulas Complex number operations Binomial theorem and factorials Conic sections All Grade 11 practice →

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