Edexcel A-Level Mathematics AS P2.5.2 Laws of Logarithms Questions

Practise applying logarithm laws to simplify expressions, solve equations and justify restrictions on possible values.

Exam points

combine log terms into one expression before forming an equation without logs
use power and quotient laws to solve for constants while rejecting invalid roots
state restrictions from log arguments and base conditions after algebraic work

[Maximum number: 4]

Given that

3 \log _{3}(2 x-1)=2+\log _{3}(14 x-25)

show that

2 x^{3}-3 x^{2}-30 x+56=0

Official answer figure

$2=\log_3 3^2$ $3\log_3(2x-1)=\log_3(2x-1)^3$

or

$\log_3 3^2+\log_3(14x-25)=\log_3(3^2(14x-25))$ $(2x-1)^3=9(14x-25)$ $8x^3-12x^2+6x-1=126x-225$ $2x^3-3x^2-30x+56=0$

A1*

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Edexcel A-Level Mathematics AS P2.5.2 Laws of Logarithms Questions question 1