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

1 Answer
Apr 15, 2018

log_20 0.125=-0.6941

Explanation:

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