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Logarithms

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Question : 20 of 85

Marks: +1, -0

If

10^{x}=1.73

\log_{10} 173=2.2380

x

is

0.2380
2.2380
1.2380
$\overline{1}.2380$

Solution:

Concept:

Use the logarithm property

\log(a/b) = \log a - \log b

to express

x

in terms of

\log_{10} 173

.

Explanation:

Given

10^x = 1.73

, taking base-10 logs gives

x = \log_{10} 1.73

.

Write

1.73 = \frac{173}{100}

. Then

x = \log_{10}\left(\frac{173}{100}\right)

.

Using the property:

x = \log_{10} 173 - \log_{10} 100

.

We know

\log_{10} 173 = 2.2380

and

\log_{10} 100 = 2

.

So

x = 2.2380 - 2 = 0.2380

.

Answer:

x = 0.2380

, which corresponds to option A.

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