How do you evaluate $log_20 0.125$ using the change of base formula?

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Answer 1 · 2018-04-15T16:14:22

$log_20 0.125=-0.6941$

According to change of base formula

$log_ab=log_xb/log_xa=logb/loga$

and when we use base $10$ , we do not write $10$ in subscript.

Hence $log_20 0.125$

= $log0.125/log20$

= $log(1/8)/log(2*10)$

= $(log1-log8)/(log2+log10)$

= $(-log2^3)/(log2+1)$

= $-(3log2)/(1+log2)$

= $-(3*0.3010)/1.3010$

= $-0.6941$

How do you evaluate log_20 0.125log_20 0.125 using the change of base formula?