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Logarithms and Their Uses Quiz

Ten Logarithms and Their Uses practice questions cover calculations and concepts. Every answer is explained.

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ByLelfy Editorial Team

For High school students and adults reviewing the topic.

About 16 minutes. 10 questions.

How does it work?

  1. Choose one answer or enter a number in the stated unit, then check it.
  2. Round only the final answer to the precision requested.

What will you get?

Review a score and an explanation for every answer.

Question 1Evaluate log₃(243) for a growth model. Enter its value as a number with no unit, rounded to the nearest whole number.

Answers within 0.5 of the expected value are accepted.

Question 2A culture model has size 7 × 2ᵗ. Find t when the modeled size reaches 896. Enter a number with no unit, rounded to the nearest whole number.

Answers within 0.5 of the expected value are accepted.

Question 3Evaluate log₅(15625/25). Enter a number with no unit, rounded to the nearest whole number.

Answers within 0.5 of the expected value are accepted.

Question 4A calculation requires log₇(90). Use change of base and enter a number with no unit, rounded to three decimal places.

Answers within 0.0005 of the expected value are accepted.

Question 5Use pH = −log₁₀(c), where c is the hydrogen-ion concentration, 0.000032 mol/L, in an illustrative solution. Find pH as a number with no unit, rounded to two decimals.

Answers within 0.005 of the expected value are accepted.

Question 6An illustrative balance grows by 7% each year. Solve 2 = 1.07ᵗ for its doubling time in years, rounded to two decimals.

Answers within 0.005 years of the expected value are accepted.

Question 7Which value equals log₇(49) + log₇(343)?
Question 8A student must evaluate log₁₀(11 + 89). Which result is correct?
Question 9Which value equals log₄(16³)?
Question 10A logarithmic axis marks equally spaced values 3, 30, and 300. What is the next value at that spacing?

Answer every question to see and share your score.

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