If #log_b 5 = .41#, what is #log_b 125#?

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Answer 1 · 2016-01-29T00:26:23

#1.23#

Note that #125=5^3#.

Thus,

#log_b(125)=log_b(5^3)#

We can now simplify this using the rule: #log_b(a^c)=c*log_b(a)#

#log_b(5^3)=3*log_b(5)#

Since #log_b(5)=0.41#, we know that

#3*log_b(5)=3*0.41=1.23#