CAIE IGCSE Additional Math 6.2 Use Laws of Logarithms Questions

Practise Cambridge IGCSE Additional Mathematics by simplifying logarithms, solving log equations and checking domain restrictions.

Exam points

Apply logarithm laws and change-of-base identities to simplify expressions.
Solve logarithmic equations with reciprocal-log and domain restrictions.
Express answers as a single logarithm or exact solution and verify admissibility.

[Maximum number: 5]

Solve the following equations.

$\log_5(5x-2)-\log_{25}x=\frac{1}{2}$

$\log_5(5x-2)^2-\log_5 x=1$ oe
B1 for $\log_{25}x=\frac{\log_5 x}{\log_5 25}=\frac{\log_5 x}{2}$
B1 for $2\log_5(5x-2)=\log_5(5x-2)^2$ oe
$\log_5\frac{(5x-2)^2}{x}=1$
M1 dep on one of the previous B1 marks;
accept $\log_5 5$ for 1.
$25x^2-25x+4=0$ oe
M1 dep for forming and attempting to solve a 3-term quadratic;
must have at least 2 B marks.
$x=\frac{4}{5}$ only
A1
Alternative methods using base 25, square-root logarithms, or common logs are accepted as in the markscheme.

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CAIE IGCSE Additional Math 6.2 Use Laws of Logarithms Questions question 1