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 bases of the logarithm and the exponent
In the given expression \( \log _{5} 5^{7} \), both the base of the logarithm and the base of the exponent are 5.
2Step 2: Apply Basic Logarithm Principle
According to the basic principle of logarithms, if the base of the logarithm and the base of the exponent are the same, the logarithm simply evaluates to the actual exponent. Therefore, \( \log _{5} 5^{7} \) equals to 7.
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