Write as a single logarithm (show steps)

1/3  log 125 can be rewritten as (1/3) log 5^3 = log 5

Similarly, 1/3 log 8 can be re-written as 1/3  log 2^3, same as (1/3)(3 log 2)= log 2

Thus, the fraction can be written in simpified form as log 5  /  log 2.

The second term is the same as log m^5.

Thus, your final result is (log 5) / (log 2) + log m^5.