Problem 39
Question
Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$
Step-by-Step Solution
Verified Answer
The value of \( \log _{5} 5^{7} \) is 7.
1Step 1: Identify the Logarithmic Expression
We have the expression \( \log _{5} 5^{7} \).
2Step 2: Apply the Logarithmic Rule
The result of the logarithm base b of b to the power of n is simply n. This is because there are n b's that multiply together to get b to the power of n. So, in this case, the answer is simply 7.
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