evaluate each expression.\n(a) $log_{5}\frac{1}{25}=$\n(b) $log_{2}32=$
evaluate each expression.\n(a) $log_{5}\frac{1}{25}=$\n(b) $log_{2}32=$
Answer
Explanation:
Step1: Recall log - rule
Let (y = \log_{a}x) is equivalent to (a^{y}=x). For (\log_{5}\frac{1}{25}), we need to find (y) such that (5^{y}=\frac{1}{25}). Since (\frac{1}{25}=5^{- 2}), then (y=-2).
Step2: Recall log - rule for second part
For (\log_{2}32), we need to find (y) such that (2^{y}=32). Since (32 = 2^{5}), then (y = 5).
Answer:
(a) - 2 (b) 5