CAIE A-Level Mathematics A2 3.2.1 Log Laws Questions

Practise logarithm laws and solving logarithmic equations within the AS mathematics syllabus.

Exam points

apply logarithm laws to combine and expand expressions
solve logarithmic equations with domain restrictions
convert logarithmic forms and give accurate numerical solutions

[Maximum number: 4]

Solve the equation $\ln (2 x-1)=2 \ln (x+1)-\ln x$ . Give your answer correct to 3 decimal places.

Use law for the logarithm of a product, quotient or power
Remove logarithms and state a correct equation, e.g. $x(2 x-1)=(x+1)^{2}$
Solve a 3-term quadratic obtaining at least one root
Obtain answer 3.303 only

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CAIE A-Level Mathematics A2 3.2.1 Log Laws Questions question 1