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Logarithms Practice Test 2

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Question : 4 of 39

Marks: +1, -0

If

\log_{10} 2 = 0.3010

\log_{10} 7 = 0.8451

, then find the value of

\log_{10} 2.8

.

0.4471
1.4471
2.4471
3.4471

Solution:

Concept:

Use logarithm rules to express

2.8

in terms of

2

,

7

, and

10

.

Explanation:

Write

2.8

as

\frac{7 \times 2^2}{10}

.

Apply the product and quotient rules of logarithms.

\log_{10} 2.8 = \log_{10}\left(\frac{7 \times 2^2}{10}\right)

= \log_{10} 7 + 2\log_{10} 2 - \log_{10} 10

Substitute

\log_{10} 2 = 0.3010

,

\log_{10} 7 = 0.8451

, and

\log_{10} 10 = 1

.

= 0.8451 + 2(0.3010) - 1

= 0.8451 + 0.6020 - 1

= 1.4471 - 1 = 0.4471

Answer:

\log_{10} 2.8 = 0.4471

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