To convert the logarithmic equation [tex]\(\log_6 18 = x\)[/tex] into its equivalent exponential form, we start by recalling the definition of a logarithm. The logarithmic equation [tex]\(\log_b a = c\)[/tex] is equivalent to the exponential equation [tex]\(b^c = a\)[/tex].
Given the logarithmic equation:
[tex]\[
\log_6 18 = x
\][/tex]
We identify the base [tex]\(b\)[/tex], the result [tex]\(a\)[/tex], and the logarithm [tex]\(c\)[/tex] as follows:
- The base [tex]\(b\)[/tex] is 6.
- The result [tex]\(a\)[/tex] is 18.
- The logarithm [tex]\(c\)[/tex] is [tex]\(x\)[/tex].
Using the definition mentioned, we rewrite the equation in exponential form:
[tex]\[
6^x = 18
\][/tex]
Therefore, the correct exponential equation that corresponds to the logarithmic equation [tex]\(\log_6 18 = x\)[/tex] is:
[tex]\[
6^x = 18
\][/tex]
Thus, the correct answer is:
C. [tex]\(6^x = 18\)[/tex]
