Express log base b of ab using x.

01 / Standard#Your turn

\log_a(ab)=x

Official paper · jm01-2026 · I.7 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

First isolate log base a of b.

Hint 2

Change the base of the requested logarithm to a.

Worked solution

The logarithms require positive bases different from one.
$a,b>0,\ a,b\ne1,\quad\log_a b=x-1\ne0$
Use change of base.
$\log_b(ab)=\frac{\log_a(ab)}{\log_a b}=\frac{x}{x-1}$

B: x/(x−1).

Checks and common pitfalls: x=1 would force b=1, which is not a logarithm base.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The logarithms require positive bases different from one.
$a,b>0,\ a,b\ne1,\quad\log_a b=x-1\ne0$
Use change of base.
$\log_b(ab)=\frac{\log_a(ab)}{\log_a b}=\frac{x}{x-1}$

Think first. Reveal a hint when the class is ready.

2026 JM01