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Logarithms Practice Test 2

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Question : 16 of 39

Marks: +1, -0

\log_5 5 \log_4 9 \log_3 2

simplifies to:

2
1
5
None of these

Solution:

Concept:

Use logarithm power and change-of-base rules to simplify the product.

Explanation:

Given expression:

\log_5 5 \cdot \log_4 9 \cdot \log_3 2

.

First,

\log_5 5 = 1

.

Now,

\log_4 9 = \log_{2^2} 3^2

.

Using the power rule:

\log_{a^m} b^n = \frac{n}{m}\log_a b

.

So,

\log_4 9 = \frac{2}{2}\log_2 3 = \log_2 3

.

Also,

\log_3 2 = \frac{1}{\log_2 3}

.

Multiply all terms:

1 \cdot \log_2 3 \cdot \frac{1}{\log_2 3} = 1

.

Answer:

The simplified value is

1

.

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