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

Practise Edexcel IAL Mathematics P2.5.2 by combining logarithms, applying power and quotient laws, solving the resulting equations and rejecting values outside each domain.

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: 6]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

(a)

Using the laws of logarithms, solve

2 \log _{2}(2-x)=4+\log _{2}(x+10)

[ 5 ]

12
B1: One correct log law seen or used.
M1: Correct attempt to combine two of the original terms, condoning a slip with 16.
A1: Correct equation not involving logs, for example $(2-x)^2=16(x+10)$ .
M1: Correct attempt to solve a 3-term quadratic in x, achieving a real root.
A1: x=-6 only;
the x=26 solution must be rejected.

(b)

Find the value of

\log _{\sqrt{a}} a^{6}

where a is a positive constant greater than 1

[ 1 ]

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

Question (a)

Question (b)