To find the exponent \(x\) that makes the two expressions equivalent, we need to solve the equation:
\[ (33)^x = 324 \]
We can take the logarithm of both sides to solve for \(x\):
\[ x \cdot \log(33) = \log(324) \]
Thus,
\[ x = \frac{\log(324)}{\log(33)} \]
Now, we can calculate \(\log(324)\) and \(\log(33)\).
First, let's find \(\log(324)\). Since \(324 = 18^2 = (3^2 \cdot 2)^2 = 3^4 \cdot 2^2\), we can also calculate it directly:
\[ \log(324) \approx 2.510825623 \]
Next, we find \(\log(33)\):
\[ \log(33) \approx 1.518513939 \]
Now, we can divide these values:
\[ x \approx \frac{2.510825623}{1.518513939} \approx 1.653 \]
Since none of your given options (15, 8, 21, 27) is close to \(1.653\), it seems there may be a misunderstanding or error in the options provided. If you wish to compare against those options assuming specific values, please clarify or provide any additional context.