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Logarithms

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Question : 62 of 85

Marks: +1, -0

If

\log 2 = 0.3010

\log_{8} 25

is

$1$
$2$
$1.5482$
None

Solution:

Concept:

Use change of base formula and given logarithm value.

Explanation:

We need

\log_{8} 25

.

Using change of base to base 10:

\log_{8} 25 = \frac{\log 25}{\log 8}

.

Given

\log 2 = 0.3010

.

Then

\log 5 = \log(10/2) = \log 10 - \log 2 = 1 - 0.3010 = 0.6990

.

So

\log 25 = \log(5^2) = 2 \log 5 = 2 \times 0.6990 = 1.3980

.

Also

\log 8 = \log(2^3) = 3 \log 2 = 3 \times 0.3010 = 0.9030

.

Thus

\log_{8} 25 = \frac{1.3980}{0.9030} \approx 1.5482

.

Answer:

1.5482

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