CAIE IGCSE Additional Math 6.2 laws of logarithms

Use this logarithm-laws page to combine log terms, change powers into coefficients and solve equations while respecting valid domains.

Exam points

Use log laws to combine sums, differences and multiples of logarithms.
Solve logarithmic equations after reducing them to algebraic equations.
Check domain restrictions so logarithm arguments remain positive before solving.

[Maximum number: 5]

Solve the equation $\log_3(y^2+11)-2=\log_3(y-1)$ .

$\log_3\left(\frac{y^2+11}{9}\right)=\log_3(y-1)$
B1
$\frac{y^2+11}{9}=y-1$
M1
$y^2-9y+20=0$
A1
Solves the quadratic
M1
y=4, y=5
A1

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