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Logarithms

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Question : 66 of 85

Marks: +1, -0

The value of

\; \frac{\log_a}{\log_a} \; \frac{\log_b a}{\log_a b}

is

$-1$
1
$\log_a b$
$\log_a(a b)$

Solution:

Concept:

Use the identity

\log_b a = 1 / \log_a b

and the property

\log_a(1/x) = -\log_a x

.

Explanation:

Write the expression as

\frac{\log_a(\log_b a)}{\log_a(\log_a b)}

.

Since

\log_b a = \frac{1}{\log_a b}

, we have

\log_a(\log_b a) = \log_a \left( \frac{1}{\log_a b} \right) = -\log_a(\log_a b)

.

Then

\frac{-\log_a(\log_a b)}{\log_a(\log_a b)} = -1

.

Answer:

-1

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