Test Index

UPSC NDA Math Model Paper 7

Question : 86 of 120

Marks: +1, -0

The value of

\left\{ \frac{1}{\log_{9} 60} + \frac{1}{\log_{16} 60} + \frac{1}{\log_{25} 60} \right\}

is -

Solution:

Given that

\left\{ \frac{1}{\log_{9} 60} + \frac{1}{\log_{16} 60} + \frac{1}{\log_{25} 60} \right\}

By base changing we can write it as -

\Rightarrow \log_{60} 9 + \log_{60} 16 + \log_{60} 25

By product rule of logarithms we can write it again as-

\Rightarrow \log_{60}(9 \times 16 \times 25) = \log_{60}(3600)

\Rightarrow \log_{60}(60)^{2} = 2 \log_{60}(60) = 2

Therefore, option (3) is the correct answer.

Go to Question:

Prev Question

Next Question