LEARN · EXPLAIN · REVISE

Evaluate by change of base.

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 / Foundation#Your turn

\log_{128}16384

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

Use base two in numerator and denominator.

Worked solution

Rewrite logarithms as exponent equations and check base and argument conditions.
Calculate or simplify this relation.
$\frac{\log_216384}{\log_2128}=\frac{14}{7}=2$
A change of base needs the same new base in both places.

The requested value is 2.

Checks and common pitfalls: A change of base needs the same new base in both places.

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

Teacher preparation and assessment