Problem 17 - College Algebra Essentials

Question

Write each equation in its equivalent logarithmic form. $$b^{3}=1000$$

Step-by-Step Solution

Answer

The logarithmic form of the equation \(b^{3}=1000\) is \(\log_{b}1000 = 3.\)

Step 1: Understand Logarithmic Form

The logarithmic form of the expression \(b^{a} = c\) can be written as \(\log_{b}c = a.\) This is based on the basic definition of logarithms.

Step 2: Apply the Logarithmic Form

Apply the logarithmic format to the given expression \(b^{3}=1000.\) So, this transforms the given expression to \(\log_{b}1000 = 3.\) Remember, in a logarithmic equation \(\log_{b}c = a,\) 'b' is the base, 'a' is exponent, and 'c' is the result.