Problem 10 - College Algebra Essentials

Question

Write each equation in its equivalent logarithmic form. $$5^{4}=625$$

Step-by-Step Solution

Answer

The equivalent logarithmic form of the equation \(5^{4}=625\) is \(\log_{5}{625} = 4\).

Step 1: Identify the base, exponent and output in exponential form

In the given equation \(5^{4}=625\), the base is 5, the exponent is 4 and the output or 'answer' is 625.

Step 2: Convert the equation to logarithmic form

To convert \(5^{4}=625\) into logarithmic form, rearrange the equation such that the base of the logarithm is 5 (the base of the power), the output of the logarithm is 4 (the exponent) and the input is 625 (the 'answer'). This gives the logarithmic form of the equation as \(\log_{5}{625} = 4\).

Step 3: Confirm the transformation is correct

In the equation \(\log_{5}{625} = 4\), the base is 5, the output is 4 and the input is 625 which matches with the given exponential equation, confirming that the transformation is correct.