A-level · Exponentials & logarithms

The laws of logarithmsExam-style questions

The product, quotient and power laws — turning sums and differences of logs into a single log (and back) — plus log_a a = 1, log_a 1 = 0 and the reciprocal rule.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
Solve the equation

$\log_2(x+5) + \log_2(x-1) = 4$ . (4 marks)
Level 2 · 4 marksTry it
2
Solve the equation

$\log_3(2x + 1) + \log_3(x - 1) = 2$

You must show clearly why any value you obtain must be rejected. (5 marks)
Level 3 · 5 marksTry it
3
Solve the equation

$2\log_2 x - \log_2 (x + 3) = 1$

giving your answer in exact form. Fully justify your answer. (5 marks)
Level 3 · 5 marksTry it
4
Solve the equation $\log_{2}(x + 3) = 2 + \log_{4}(x + 6)$ . Give your answer correct to 2 decimal places.

(4 marks)
Level 3 · 4 marksTry it
5
The positive numbers $x$ and $y$ satisfy the equation

$\log_3 x^2 - \log_3 y^5 = 4$

Express $x$ in terms of $y$ , giving your answer in the form $x = Ay^p$ , where $A$ and $p$ are constants.

(4 marks)
Level 3 · 4 marksTry it

7 more questions on the laws of logarithms

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