Problem 8 - College Algebra

Question

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

Step-by-Step Solution

Answer

The equivalent exponential form of the equation is \(5^y = 125\).

Step 1: Recap logarithmic and exponential functions

The key to solve this task is understanding how logarithmic and exponential functions are related. In the general form, a logarithmic equation \(\log_{b}a = x\) can be converted to an exponential equation in the form of \(b^x = a\).

Step 2: Identify the components

Looking at the given equation, the base (b) is 5, the exponent (x) is y, and the result (a) of the function is 125.

Step 3: Conversion to Exponential form

Using the understanding of these components from the previous step, now write the equation in its exponential form: \(5^y = 125\)