If ₁0}1995 = 3.3000, then what is the value of (0.001995)¹/8}?

Correct Answer is : 1100.3375{1}{10^{0.3375}}100.33751

Correct Answer is : 1100.3375{1}{10^{0.3375}}100.33751

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UPSC CDS 2 2019 Math Paper

Question : 58 of 100

Marks: +1, -0

\log_{10}1995 = 3.3000

(0.001995)^{1/8}

Solution:

Concept:

Use logarithms to simplify exponent and fractional powers.

Explanation:

Let

X = (0.001995)^{1/8}

Take log base 10 on both sides:

\log_{10} X = \frac{1}{8} \log_{10}(0.001995)

Write

0.001995 = 1995 \times 10^{-6}

Then

\log_{10}(1995 \times 10^{-6}) = \log_{10}1995 + \log_{10}10^{-6}

Substitute given

\log_{10}1995 = 3.3000

and

\log_{10}10^{-6} = -6

= 3.3000 - 6 = -2.7000

Thus

\log_{10} X = \frac{1}{8} \times (-2.7) = -0.3375

Hence

X = 10^{-0.3375} = \frac{1}{10^{0.3375}}

Answer:

Option B:

\frac{1}{10^{0.3375}}

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