Problem 18 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The equivalent logarithmic form of the equation \( b^{3} = 343 \) is \( \log_b 343 = 3 \)

Step 1: Understand the exponential form

We first look at the given equation which is in exponential form, \( b^3 = 343 \). Here, 'b' is the base, '3' is the exponent, and '343' is the result.

Step 2: Applying the logarithmic conversion rule

According the rule of conversion from exponential form to logarithmic form, if \( b^3 = 343 \) , then its equivalent in logarithmic form would be \( \log_b 343 = 3 \). It simply expresses the operation which is 'b raised to what power results in 343'.