Solve the following: (x^2+ 36) - 2 x = 1 - Vidyadip

Question

Solve the following:$\log(x^2+ 36) - 2\log x = 1$

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Answer

$\log \left(x^2+36\right)-2 \log x=1$
$\Rightarrow \log \left(x^2+36\right)-\log x 2=1$
$\Rightarrow \log \left(\frac{x^2+36}{x^2}\right)=1$
$=\log 10$
$\Rightarrow\left(\frac{x^2+36}{x^2}\right)=10$
$\Rightarrow x^2+36=10 x^2$
$\Rightarrow 9 x^2=36$
$\Rightarrow x^2=4$
$\Rightarrow x=2 .$

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