Certainly! Let's start with the given logarithmic equation:
[tex]\[
\log (3x + 9) = \frac{1}{3}
\][/tex]
To convert this logarithmic equation into its exponential form, we need to understand that the logarithmic form [tex]\(\log_b(a) = c\)[/tex] is equivalent to the exponential form [tex]\(a = b^c\)[/tex]. Here, the base [tex]\(b\)[/tex] is 10, as it's implied when the base is not specified. Therefore, we can rewrite the equation as:
[tex]\[
3x + 9 = 10^{\frac{1}{3}}
\][/tex]
So, in exponential form, the equation is:
[tex]\[
3x + 9 = 10^{\frac{1}{3}}
\][/tex]
This is the exponential form of the given logarithmic equation.
