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  4. If N =(2 log 70 9800)(5 log 70 140)(7 log 70 2), then N is equal to

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Q. If $N =\left(2^{\log _{70} 9800}\right)\left(5^{\log _{70} 140}\right)\left(7^{\log _{70} 2}\right)$, then $N$ is equal to

Continuity and Differentiability

Solution:

$N =\left(2^{\log _{70}\left((70)^2 \times 2\right)}\right)\left(5^{\log _{70}(70 \times 2)}\right)\left(7^{\log _{70} 2}\right)=\left(2^{2+\log _{70} 2}\right)\left(5^{1+\log _{70} 2}\right)\left(7^{\log _{70} 2}\right)$
$=20(2 \times 5 \times 7)^{\log _{70} 2}=20\left(70^{\log _{70} 2}\right)=20 \times 2=40$.