Find 1/a+1/b.

01 / Standard#Your turn

2^a=5^b=\sqrt{10}

Official paper · jm01-2022 · I.6 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Take logarithms in each equality.

Hint 2

The reciprocal exponents share the same denominator.

Worked solution

Express the reciprocals.
$\frac1a=\frac{\ln2}{\ln\sqrt{10}},\quad\frac1b=\frac{\ln5}{\ln\sqrt{10}}$
Combine using ln2+ln5=ln10.
$\frac1a+\frac1b=\frac{\ln10}{(1/2)\ln10}=2$

A: 2.

Checks and common pitfalls: The common value is √10, so its logarithm is half ln10.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Express the reciprocals.
$\frac1a=\frac{\ln2}{\ln\sqrt{10}},\quad\frac1b=\frac{\ln5}{\ln\sqrt{10}}$
Combine using ln2+ln5=ln10.
$\frac1a+\frac1b=\frac{\ln10}{(1/2)\ln10}=2$

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

2022 JM01