Problem 18 - College Algebra

Question

Write each equation in its equivalent logarithmic form. $$b^{3}=343$$

Step-by-Step Solution

Answer

The logarithmic form of the given equation \(b^{3}=343\) is \(\log_{b}(343)=3\).

Step 1: Identify the base, exponent, and result

In the given exponential equation, \(b^{3}=343\), 'b' is the base, '3' is the exponent, and '343' is the result.

Step 2: Write in logarithmic form

An equivalent logarithmic equation has the form: \(\log_{base}(result)=exponent\). In this case, the base is \(b\), the exponent is \(3\), and the result is \(343\). Substitute these values in to get the logarithmic equation.

Step 3: Write the final equation

Substituting the identified values into the logarithmic form, the final equation becomes \(\log_{b}(343)=3\).