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Find the value of x if 14 {10^{ - 4}} = {{500} x}

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Find the value of $x$ if $14 \times 1 0^{- 4} = lo g \frac{500}{x}$

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Find the value of

x

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14 \times 1 0^{- 4} = lo g \frac{500}{x}

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Text solutionVerified

Given,

\Rightarrow 14 \times 1 0^{- 4} = lo g \frac{500}{x}

\Rightarrow 14 \times 1 0^{- 4} = lo g_{10} 500 - lo g_{10} x \dots (lo g (\frac{a}{b} = lo g a - lo g b))

\Rightarrow 14 \times 1 0^{- 4} = lo g_{10} (5 \times 100) - lo g_{10} x

\Rightarrow 14 \times 1 0^{- 4} = lo g_{10} 5 + lo g_{10} 1 0^{2} - lo g_{10} x

\Rightarrow 14 \times 1 0^{- 4} = lo g_{10} 5 + 2 lo g_{10} 10 - lo g_{10} x \dots (n lo g_{a} b = lo g_{a} b^{n})

\Rightarrow lo g_{10} x = lo g_{10} 5 + 2 - \frac{14}{1 0 ^{4}}

\Rightarrow lo g_{10} x = lo g_{10} 5 + 2 - \frac{14}{1 0 ^{4}}

\Rightarrow x = 1 0^{l o g_{10} 5} + 1 0^{2} - 1 0^{\frac{14}{104}}

\Rightarrow x = 5 + 100 - 1 0^{14 \times 1 0^{- 4}}

\Rightarrow x = 105 - 1 0^{14 \times 1 0^{- 4}}

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Question Text	Find the value of $x$ if $14 \times 1 0^{- 4} = lo g \frac{500}{x}$
Answer Type	Text solution:1
Upvotes	150