Question

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.  
log Subscript 6 Baseline x equals 2
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Part 1
Solve the equation. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is StartSet nothing EndSet .
  
​(Simplify your​ answer.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

To solve the logarithmic equation \( \log_6(x) = 2 \), we can rewrite it in its exponential form. The equation states that \( x \) is the value raised to the base of the logarithm (which is 6) equals \( 6^2 \).

So, we can convert the logarithmic equation as follows:

\[
x = 6^2
\]

Calculating \( 6^2 \):

\[
x = 36
\]

We also need to ensure that \( x = 36 \) is within the domain of the original logarithmic expression. The logarithm function \( \log_6(x) \) is only defined for \( x > 0 \). Since \( 36 \) is positive, it lies within the domain.

Thus, the solution to the equation is:

\[
x = 36
\]

Now, corresponding to the options provided:

A. The solution set is {36}.

So, the complete answer is:

**A. The solution set is {36}.**