Find value of 0.0625 to the base 2 . - Vidyadip

Question

Find value of $\log 0.0625$ to the base 2 .

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Answer

$\log _2 0.0625=\log _2 \frac{625}{10000}$
$\begin{array}{l}=\log _2 \frac{5^4}{10^4} \\ =\log _2\left(\frac{5}{10}\right)^4 \\ =4 \log _2\left(\frac{1}{2}\right)\end{array}$
[Applying rule $\log _a m^n=n \log _a m$ ]
$=4\left[\log _2 1-\log _2 2\right]$
[Applying rule $\log _a\left(\frac{m}{n}\right)=\log _a m-\log _a{ }^n$ ]
$=4[0-1]$
[Applying rule $\log _a 1=0$ and $\log _a a=1$ ]
$=-4$

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