Question: log 5 (25*5^-3) : log sub 5 : how is the answer: -1 ?
Let n = log_5[25*5^(-3)]
Take the expression inside the square brackets. We have 25*5^(-3)
and 5^(-3) = 1/(5^3) = 1/125
So 25*5^(-3) = 25*(1/125) = 1/5
and 1/5 = 5^(-1).
Our log expression then becomes log_5[5^(-1)] = n
Now, by definition, if log_a[b] = x, then b = x^a.
Since we have log_5[5^(-1)] = n, then, by definition, 5^(-1) = 5^n.
From which it follows: n = -1