Test Index

Logarithms

© examsnet.com

Question : 80 of 85

Marks: +1, -0

The value of of

(\log_b a \: \log_c b \: \log_a c)^3 =

1
3
$(\log_b C)^3$
$(\log_c b)^3$

Solution:

Concept:

Using the change-of-base formula for logarithms to simplify the product.

Explanation:

Write each logarithm with a common base, say base 10:

\log_b a = \frac{\log a}{\log b}

,

\log_c b = \frac{\log b}{\log c}

,

\log_a c = \frac{\log c}{\log a}

.

Multiply them:

\frac{\log a}{\log b} \cdot \frac{\log b}{\log c} \cdot \frac{\log c}{\log a} = 1

.

Then cube the result:

(1)^3 = 1

.

Answer:

1

© examsnet.com

Go to Question:

Prev Question

Next Question