CAIE A-Level Mathematics AS 2.2.1 Log Laws Questions

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

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[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
Confirm $x=\sqrt{\frac{9}{x+2}}$
AG;
condone absence of justification for choice of positive root.

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CAIE A-Level Mathematics AS 2.2.1 Log Laws Questions question 1