To solve the given logarithmic equation [tex]\(\log_6 18 = x\)[/tex] correctly, let's follow the appropriate steps to rewrite it as an exponential equation. Here is the process:
1. Understand the logarithmic form:
The equation [tex]\(\log_6 18 = x\)[/tex] means that [tex]\(x\)[/tex] is the power to which the base 6 must be raised to obtain 18.
2. Convert the logarithmic equation to exponential form:
The general form for converting a logarithmic equation [tex]\(\log_b a = c\)[/tex] to its equivalent exponential form is:
[tex]\[ b^c = a \][/tex]
Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(a\)[/tex] is the result, and [tex]\(c\)[/tex] is the exponent.
3. Apply this to the given equation:
- The base [tex]\(b\)[/tex] is 6.
- The exponent [tex]\(c\)[/tex] is [tex]\(x\)[/tex].
- The result [tex]\(a\)[/tex] is 18.
Rewriting this in exponential form, we get:
[tex]\[
6^x = 18
\][/tex]
4. Identify the correct answer:
Among the given options:
[tex]\[
\begin{array}{llll}
\text{A.} & x^{18} = 6 & \quad \text{(Incorrect)} \\
\text{B.} & x^6 = 18 & \quad \text{(Incorrect)} \\
\text{C.} & 6^x = 18 & \quad \text{(Correct)} \\
\text{D.} & 18^x = 6 & \quad \text{(Incorrect)} \\
\end{array}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{C. \ 6^x = 18}
\][/tex]
