Lemmara logoLemmaraWorked solution

0606/11 May/Jun 2026, Question 8: Solving Exponential and Log Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Three logarithm problems: evaluate lg(10000), solve a nested log equation, and solve an equation with log base x on both sides.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

State the value of lg(10000).

  1. 110000 = 10⁴, so lg(10000) = 4

Answer4

Part (b) · 3 marks

Find x satisfying log₂(log₃ x) = 2.

  1. 1log₃ x = 2² = 4
  2. 2x = 3⁴ = 81

Answerx = 81

Part (c) · 4 marks

Find x satisfying log_x 5 = log₅ x⁴.

  1. 1log_x 5 = 1/log₅ x and log₅ x⁴ = 4 log₅ x
  2. 21/log₅ x = 4 log₅ x
  3. 3(log₅ x)² = 1/4, so log₅ x = ±1/2
  4. 4x = 5^(1/2) = √5 or x = 5^(−1/2) = 1/√5

Answerx = √5, x = 1/√5

Stuck on a step? Read the free lesson: Solving Exponential and Log Equations

Practise more solving exponential and log equations questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on solving exponential and log equations

Also searched as: 0606/11/M/J/26 · 0606_s26_qp_11 · 0606 s26 11 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.