Problem 12
Question
Write each equation in its equivalent logarithmic form. $$5^{-3}=\frac{1}{125}$$
Step-by-Step Solution
Verified Answer
The logarithmic form of the given equation \(5^{-3}=\frac{1}{125}\) is \(\log_5{\frac{1}{125}} = -3\)
1Step 1: Identify Base, Exponent, and Output
In the given equation \(5^{-3}=\frac{1}{125}\), the base is 5, -3 is the exponent and the output or result of the expression is \(\frac{1}{125}\).
2Step 2: Conversion to Logarithmic Form
The given equation can be represented in logarithmic form as \(\log_b a = c\), where b is the base, c is the exponent and a is the output. So, replacing b with 5, c with -3 and a with \(\frac{1}{125}\), it results in \(\log_5{\frac{1}{125}} = -3\)
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Problem 12
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