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Chapter 4: Problem 12

Write each equation in its equivalent logarithmic form. $$5^{-3}=\frac{1}{125}$$

Short Answer

Expert verified
The logarithmic form of the equation \(5^{-3}=\frac{1}{125}\) is \(\log_5 (\frac{1}{125}) = -3\).

Step by step solution

01

Identify the Base

Looking at the equation \(5^{-3}=\frac{1}{125}\), we can determine the base to be 5.
02

Identify the Exponent

The exponent in the equation \(5^{-3}=\frac{1}{125}\) is -3.
03

Identify the Result

In the equation \(5^{-3}=\frac{1}{125}\), the result is \(\frac{1}{125}\).
04

Rewrite in Logarithmic Form

Using the formula \(\log_a c = b\), substitute a with 5 (the base), b with -3 (the exponent) and c with \(\frac{1}{125}\) (the result). This provides the solution in logarithmic form: \(\log_5 (\frac{1}{125}) = -3\).

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Most popular questions from this chapter

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