Problem 12 - Introductory and Intermediate Algebra for College Students 4th

Question

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

Step-by-Step Solution

Answer

The equivalent logarithmic form of \(5^{-3} = \frac{1}{125}\) is \(log_5(\frac{1}{125}) = -3 \)

Step 1: Identification

Identify the base, exponent and result in the given equation. Here, 5 is the base, -3 is the exponent and \(\frac{1}{125}\) is the result.

Step 2: Apply the conversion rule

The conversion rule from exponential form to logarithmic form is: \(a^b = c\) changes to \(log_a c = b\). Apply this rule to the given equation. So, \(5^{-3} = \frac{1}{125}\) changes to \(log_5(\frac{1}{125}) = -3 \)

Step 3: Simplification (if needed)

In this case, no further simplification is required as the above equation is in its simplest form.