Problem 7 - College Algebra Essentials

Question

Write each equation in its equivalent exponential form. $$\log _{6} 216=y$$

Step-by-Step Solution

Answer

The equivalent exponential form for the given logarithmic equation is \( 6^y = 216 \).

Step 1: Identify the base, argument, and value of the logarithmic equation

Here, we have the logarithmic equation \( \log _{6} 216=y \). From this equation, 6 is the base, y is the value, and 216 is the argument.

Step 2: Convert to exponential form

To convert this logarithmic equation into an equivalent exponential form, we use the base of 6, let the value y be the exponent, and then the argument 216, will provide us with the result. Hence, the equivalent exponential form is \( 6^y = 216 \)