Question

The product, $\log_a b\cdot\log_b a$ is equal to:

$1$

$a$

$b$

$ab$

none of these

Answer: A

Concepts:logarithms change of base

Difficulty rating: 1180

Small Hint:

Use the change-of-base formula on both logarithms

Big Hint:

The two resulting fractions are reciprocals

Solution:

For permissible bases and arguments, $\begin{aligned} \log_a b\cdot\log_b a &=\frac{\log b}{\log a}\\ &\quad{}\cdot\frac{\log a}{\log b}\\ &=1. \end{aligned}$

Thus, the correct answer is A.

1953 AMC 12 Problem 39

Answer: A

Difficulty rating: 1180

Small Hint:

Big Hint:

Solution:

Problem 39 in Other Years