Problem 7 - College Algebra

Question

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

Step-by-Step Solution

Answer

The exponential form of the equation is \( 6^y = 216 \).

Step 1: Understanding Logarithmic to Exponential Form Conversion

The exponential form of a logarithmic equation is found by raising the base value of the logarithm to the output value of the logarithm, which equals to the input value. The generalised form of the logarithmic equation is \( \log _{b} a = c \), which can be written in its exponential equivalent form as \( b^c = a \).

Step 2: Apply the Conversion For Given Equation

The given equation is \( \log _{6} 216 = y \). Using the conversion rule, it can be rewritten as \( 6^y = 216 \).