Problem 8 - College Algebra Essentials

Question

Write each equation in its equivalent exponential form. $$\log _{5} 125=y$$

Step-by-Step Solution

Answer

The equivalent exponential form of \(\log_{5} 125 = y\) is \(5^y = 125\).

Step 1: Understand the original logarithmic equation

Given the logarithmic equation \(\log _{5} 125=y\). Here, 5 is the base, 125 is the number and y is the logarithmic value.

Step 2: Write the equation in exponential form

Using the conversion rule, find the corresponding exponential equation to \(\log_{5} 125 = y\). The base of the logarithm (5) becomes the base of the exponential equation. The logarithmic value (y) is the exponent, and the number (125) is the result of the exponentiation. Thus, the exponential equation is \(5^y = 125\).