Answer:
a = -3
Explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125