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  4. If log 6=0.778 and (100)x=6, then find the value of x.

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Q. If $\log 6=0.778$ and $(100)^x=6$, then find the value of $x$.

Logarithm

Solution:

$ (100)^x=6 $
$\Rightarrow (10)^{2 x}=6$
Taking log on both sides,
$\Rightarrow 2 x(\log 10)=\log 6 $
$\Rightarrow 2 x=0.778 \text { (given: } \log 6=0.778 \text { ) } $
$\therefore x=0.389$