Question
Find $x,$ if : $log_x 625 = - 4$
✓
Answer
$\log _x 625=-4$
$\Rightarrow 625=x^{-4} \ldots[$ Removing logarithm $]$
$\Rightarrow 5^4=\left(\frac{1}{x}\right)^4$
$\Rightarrow 5=\frac{1}{x} ....[$ Powers are same$,$ bases are equal $]$
$\Rightarrow x=\frac{1}{5}$
$\Rightarrow 625=x^{-4} \ldots[$ Removing logarithm $]$
$\Rightarrow 5^4=\left(\frac{1}{x}\right)^4$
$\Rightarrow 5=\frac{1}{x} ....[$ Powers are same$,$ bases are equal $]$
$\Rightarrow x=\frac{1}{5}$
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