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Logarithms Practice Test 2

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Question : 19 of 39

Marks: +1, -0

If

a = \log_3 5, b = \log_{17} 25

, which one of the following is correct?

a < b
a = b
a > b
None of these

Solution:

Concept:

To compare logarithms with different bases, convert them to a common base.

Explanation:

Given

a = \log_3 5

and

b = \log_{17} 25

.

Rewrite

b

:

b = \log_{17} 5^2 = 2\log_{17}5 = \frac{2}{\log_5 17}

.

Rewrite

a

:

a = \log_3 5 = \frac{1}{\log_5 3} = \frac{2}{\log_5 9}

.

Since

17 > 9

, we have

\log_5 17 > \log_5 9

.

So

\frac{2}{\log_5 17} < \frac{2}{\log_5 9}

.

Therefore

b < a

, which means

a > b

.

Answer:

a > b

, so option C is correct.

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