Final answer:
The logarithmic expression log_(1/5)625 = -4 can be rewritten using base change formula, resulting in the equivalent expression 4 / (-1) = -4.
Step-by-step explanation:
The question is asking to change a logarithmic expression to an equivalent expression involving a different logarithm. Specifically, we have log_(1/5)625 = -4, and we want to express this using another logarithm base. To do so, we use the property that for any base b and number x, log_b(x) = log_k(x) / log_k(b) where k is a new base we choose.
Starting from log_(1/5)625 = -4, we can write this as 625 = (1/5)-4.
Since (1/5)-4 = 54, we have 625 = 54.
We can then use the base change formula: log_(1/5)625 = log_k625 / log_k(1/5). By choosing k=5, we get log_5625 / log_5(1/5), which simplifies to 4 / (-1) = -4, because log_5625 = 4 and log_5(1/5) = -1.