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`log_125(625)` Evaluate the logarithm.

`log_125 (625)`


To evaluate, factor 625.


`=log_125 (5^4)`


Then, apply the formula of change base `log_b(a) = (log_c(a))/(log_c(b))` .


`= (log_5 (5^4))/(log_5 (125))`


`= (log_5 (5^4))/(log_5 (5^3))`


Also, apply the rule `log_b (a^m) = m*log_b(a)` .


`= (4* log_5(5))/(3*log_5 (5))`


Take note that when the base and argument of logarithm are the same, it results to 1, `log_b(b) = 1` .


`= (4*1)/(3*1)`


`=4/3`


Therefore, `log_125 (625)=4/3` .

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