LEARN · EXPLAIN · REVISE

Evaluate the logarithm with a base below one.

Read the idea, work independently, then explain what changed.

TOPIC 01

Exponential and logarithmic functions: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

\log_{1/8}64

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Rewrite logarithms as exponent equations and check base and argument conditions.

Hint 2

A negative exponent turns the small base into a large value.

Worked solution

Rewrite logarithms as exponent equations and check base and argument conditions.
Calculate or simplify this relation.
$(1/8)^{-2}=64$
Positive arguments can have negative logarithms.

The requested value is -2.

Checks and common pitfalls: Positive arguments can have negative logarithms.

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

Teacher preparation and assessment