Question 1

Express log 4 + log 25 as a single base-10 logarithm, and state its exact value.

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Question 2

Express log 50 + log 20 as a single base-10 logarithm, and state its exact value.

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Question 3

Write 2 log x + 3 log y as a single logarithm.

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Question 4

Solve 2^(x+1) = 16.

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Question 5

Given that log 2 = p (base 10), find log 16 in terms of p.

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Question 6

Simplify (a^(5/2) × a^(1/2)) ÷ a, expressing your answer as a single power of a.

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Question 7

Write ln 12 − 2 ln 2 as a single logarithm in the form ln k.

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Question 8

Evaluate log₂₇ 9 without a calculator.

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Question 9

Write log₃(9x⁵) as a sum of simpler logarithms.

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Question 10

Given that log 2 = p and log 7 = q (base 10), write log 28 in terms of p and q.

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Question 11

Given that log 3 = a and log 5 = b (base 10), write log 45 in terms of a and b.

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Question 12

Evaluate log₄ 32 without a calculator.

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Question 13

Evaluate 32^(3/5) without a calculator.

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Question 14

Solve 8ˣ = 32.

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Question 15

Solve 100e^(0.2x) = 250, giving an exact answer.

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Question 16

Solve log₃(2x − 1) = 4.

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Question 17

Write (3√x)/x² as a single power of x, in the form a xⁿ.

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Question 18

Given that k^(3/4) = 8, find the value of k.

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Question 19

Given that log_a 6 = 1.6 and log_a 2 = 0.6, find log_a 3.

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Question 20

Given that log_a 2 = x, write log_a(8a) in terms of x.

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Topic 1.7: Laws of Exponents and Logarithms Questions

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