Select the correct answer.

Which exponential equation correctly rewrites this logarithmic equation?

[tex]\log _6 18=x[/tex]

A. [tex]x^{18}=6[/tex]
B. [tex]x^6=18[/tex]
C. [tex]6^x=18[/tex]
D. [tex]18^x=6[/tex]



Answer :

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]