How do you evaluate $log 0.01$ $log0.01$ ?

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How do you evaluate $log 0.01$ $log0.01$ ?

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Answer 1 · 2016-03-22T21:28:54

$log 0.01$ $log 0.01$ $= - 2$ $=-2$

Explanation:

$log 0.01$ $log 0.01$
$= log (\frac{1}{100})$ $=log (1/100)$
$= log (\frac{1}{10^{2}})$ $=log (1/10^2)$
$= {log 10}^{- 2}$ $=log 10^-2$ -> use property $x^{- n} = \frac{1}{x^{n}}$ $x^-n=1/x^n$
$= - 2 log 10$ $=-2 log 10$ -> use property ${log}_{b} x^{n} = n {log}_{b} x$ $log_b x^n = n log_b x$
$= - 2 (1)$ $=-2(1)$ -> log 10 = 1
$= - 2$ $=-2$

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How do you evaluate $log 0.01$ $log0.01$ ?

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