JEE MainMathematicsEasyLogarithm and its applications

Which one of the following is the smallest?

Show answer and solution

\sqrt{\log_{10}\pi^{2}}

let

\log_{10}{\ \pi = t}

= 0.5

\sqrt{2\log_{10}^{n}} = \sqrt{2t} = 1

\frac{1}{t^{3}} = 2^{3} = 8

\frac{1}{\log_{10}(x)\frac{1}{2}\ } = \frac{2}{\log_{10}\ x} = \frac{2}{t} = 4

\Rightarrow \log_{10}x \cong 0 \cdot 5

is the smallest.

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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