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UPSC CDS 1 2020 Math Paper

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Question : 21 of 100

Marks: +1, -0

If

\log x

1.25

y = x^{\log x}

\log y

equal to?

4.25
2.5625
1.5625
1.25

Solution:

Concept:

Using the power rule of logarithms:

\log(a^b) = b \log a

.

Explanation:

Given

\log x = 1.25

and

y = x^{\log x}

.

Take

\log

on both sides of

y = x^{\log x}

:

\log y = \log\left(x^{\log x}\right)

.

Apply the power rule:

\log y = (\log x) \cdot (\log x) = (\log x)^2

.

Substitute

\log x = 1.25

:

\log y = (1.25)^2 = 1.5625

.

Answer:

\log y = 1.5625

, which corresponds to option C.

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