CAIE A-Level Mathematics 2.2.1 Logarithm Laws

Practise using product, quotient and power laws to combine logarithms, remove them and solve resulting algebraic equations while enforcing positive logarithm arguments.

Exam points

combine log terms into one logarithm using the correct product, quotient or power law
equate positive arguments after removing equal logarithms and solve the resulting equation
reject any algebraic root that makes a logarithm argument zero or negative

[Maximum number: 3]

$5 \quad$ (a) Given that $2 \ln (x+1)+\ln x=\ln (x+9)$ , show that $x=\sqrt{\frac{9}{x+2}}$ .

Use the power law correctly
*M1
Use correct process to obtain equation with no logarithms
DM1
Confirm $x=\sqrt{\frac{9}{x+2}}$
A1
AG; condone absence of justification for choice of positive root.

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2.2.1—Log laws question 1