Question
Find the value of: $\log _{0.01}10$
✓
Answer
$\log _{0.01} 10$
Let $\log _{0.01} 10=x$
$\Rightarrow(0.01)^x=10$
$\Rightarrow(10-2)^x=10^1$
$\Rightarrow 10^{-2 x}=10^1$
$\Rightarrow x=-\frac{1}{2}$
$\therefore-2 x=1 .$
Let $\log _{0.01} 10=x$
$\Rightarrow(0.01)^x=10$
$\Rightarrow(10-2)^x=10^1$
$\Rightarrow 10^{-2 x}=10^1$
$\Rightarrow x=-\frac{1}{2}$
$\therefore-2 x=1 .$
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