The logarithm of $0.0625$ to the base $2$ is______________?

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Solution

Explanation:
$\log_{2} 0.0625 = \log_{2} \frac{625}{10000} \Rightarrow = \log_{2} \frac{5}{80} \Rightarrow = \log_{2} \frac{1}{16} \Rightarrow = \log_{2} \frac{1}{2^{4}} \Rightarrow = \log_{2} 2^{- 4} \Rightarrow = - 4 \log_{2} 2 [∵ \log_{b} b = 1] \Rightarrow = - 4$
Hence, the logarithm of $0.0625$ to the base $2$ is $- 4$ .

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