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Logarithms Practice Test 1

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Question : 2 of 40

Marks: +1, -0

If

\log_{10} 2 = 0.3010

, then find the value of

\log_{10} 5

.

0.5990
0.6990
0.7090
0.7290

Solution: 👈: Video Solution

Concept:

Use the logarithm quotient rule:

\log_a\left(\frac{m}{n}\right)=\log_a m-\log_a n

.

Explanation:

Write

5

as

\frac{10}{2}

.

So,

\log_{10}5=\log_{10}\left(\frac{10}{2}\right)

.

Apply the quotient rule:

\log_{10}5=\log_{10}10-\log_{10}2

.

Since

\log_{10}10=1

and

\log_{10}2=0.3010

,

\log_{10}5=1-0.3010=0.6990

.

Answer:

\log_{10}5=0.6990

.

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