Evaluate the logarithm product.

01 / Standard#Your turn

\log_9 125\,\log_{12}17\,\log_{25}3\,\log_{17}12

Official paper · jm01-2023 · I.3 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Cancel reciprocal change-of-base factors.

Hint 2

Write 9,125,25 as powers.

Worked solution

The middle reciprocal pair multiplies to one.
$\log_{12}17\log_{17}12=1$
Convert the remaining pair to natural logarithms.
$\frac{3\ln5}{2\ln3}\frac{\ln3}{2\ln5}=\frac34$

C: 3/4.

Checks and common pitfalls: Apply powers to both bases and arguments.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The middle reciprocal pair multiplies to one.
$\log_{12}17\log_{17}12=1$
Convert the remaining pair to natural logarithms.
$\frac{3\ln5}{2\ln3}\frac{\ln3}{2\ln5}=\frac34$

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

2023 JM01