Lemmara logoLemmaraWorked solution

4PM1/01 Jun 2024, Question 9: The Laws of Logarithms

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Logarithm question: find a base from a log equation, prove a log identity involving 3x log₂ x, 4 log₁₆ 8 and 6x log₄ 8, then solve the resulting equation equal to 0.

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

Part (a) · 2 marks

Find the value of a for which log_a 8 equals 3/4.

  1. 1a^(3/4) = 8
  2. 2a = 8^(4/3) = (∛8)⁴ = 16

Answera = 16

Part (b) · 4 marks

Show that the given expression with 3x log₂ x, 4 log₁₆ 8, 6x log₄ 8 and log₂ x equals log₂ (8x)^(3x − 1).

  1. 14 log₁₆ 8 = 4 log₂ 8/log₂ 16 = log₂ 8
  2. 26x log₄ 8 = 6x log₂ 8/log₂ 4 = 3x log₂ 8
  3. 3LHS = 3x log₂ x − log₂ 8 + 3x log₂ 8 − log₂ x
  4. 4= (3x − 1)log₂ x + (3x − 1)log₂ 8
  5. 5= (3x − 1)log₂ 8x = log₂ (8x)^(3x − 1)

Answer3x log₂ x − 4 log₁₆ 8 + 6x log₄ 8 − log₂ x = log₂ (8x)^(3x − 1) shown

Part (c) · 3 marks

Using part b, solve the equation formed when that expression equals 0.

  1. 1(3x − 1)log₂ 8x = 0
  2. 23x − 1 = 0 gives x = 1/3
  3. 38x = 1 gives x = 1/8

Answerx = 1/3, x = 1/8

Stuck on a step? Read the free lesson: The Laws of Logarithms

Practise more the laws of logarithms questions

Real 4PM1 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 the laws of logarithms

Also searched as: 4PM1 1 June 2024 · 4PM1/01 · 4pm1 jun24 1 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.