If frac{1}{log _{x} 10}=frac{2}{log _{a} 10}- | vedclass

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Question

(D) Given the equation: $\frac{1}{\log _{x} 10}=\frac{2}{\log _{a} 10}-2$Using the property $\frac{1}{\log _{b} a} = \log _{a} b$,we get:$\log _{10} x

Vedclass · Accepted Answer

$a^{2} / 100$

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(D) Given the equation: $\frac{1}{\log _{x} 10}=\frac{2}{\log _{a} 10}-2$Using the property $\frac{1}{\log _{b} a} = \log _{a} b$,we get:$\log _{10} x = 2 \log _{10} a - 2$$\log _{10} x = 2 (\log _{10} a - 1)$Since $1 = \log _{10} 10$,we can write:$\log _{10} x = 2 (\log _{10} a - \log _{10} 10)$Using the quotient rule $\log m - \log n = \log (m/n)$:$\log _{10} x = 2 \log _{10} (a/10)$Using the power rule $n \log m = \log (m^n)$:$\log _{10} x = \log _{10} (a/10)^2$$\log _{10} x = \log _{10} (a^2 / 100)$Therefore,$x = a^2 / 100$.

If $\frac{1}{\log _{x} 10}=\frac{2}{\log _{a} 10}-2,$ then $x=$

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