If $2^{x} {.3}^{2 x} = 100$ (Given $l o g 2 = 0.3010$ and $l o g 3 = 0.4771$ ), then the value of $x$ is

1.49

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1.59

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1.69

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1.79

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Solution

The correct option is B $1.59$
$T h e g i v e n e q u a t i o n i s 2^{x} . 3^{2 x} = 100 t a k i n g l o g a r i t h m f o r b o t h t h e s i d e s, w e h a v e l o g 2^{x} {.3}^{2 x} = l o g 100 \Rightarrow l o g 2^{x} + l o g 3^{2 x} = 2 (∵ l o g 100 = 2) \Rightarrow x l o g 2 + 2 x l o g 3 = 2 \Rightarrow x (l o g 2 + 2 l o g 3) = 2 \Rightarrow x (.3010 + 2 \times .4771) = 2 \Rightarrow x = \frac{2}{1.2552} = 1.593 = 1.59 (A n s)$

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