Final answer:
The change of base formula allows us to evaluate logarithms with bases that may not be given on our calculator. To evaluate log base 8 of 25, we can use the change of base formula with any base that our calculator supports.
Step-by-step explanation:
The change of base formula allows us to evaluate logarithms with bases that may not be given on our calculator. The formula states that:
logab = logcb / logca
To evaluate log825, we can use this formula with any base that our calculator supports. Let's choose base 10:
log1025 / log108
Using the property that log(a) = log(b) - log(c), we can rewrite this as:
(log1025) / (log102) - (log108) / (log102)
This can be simplified to:
log1025 / 3 - 1 = 0.3979