To find the value of \( \log 81 \), we can express 81 in terms of a base that can be easily worked with. We know that:
\[ 81 = 3^4 \]
Using properties of logarithms, we can rewrite the logarithm:
\[ \log 81 = \log (3^4) \]
Using the power rule of logarithms, which states that \( \log(a^b) = b \cdot \log(a) \), we have:
\[ \log (3^4) = 4 \cdot \log 3 \]
If we need to find a numerical value and assuming the base of the logarithm is 10 (common logarithm) or base \( e \) (natural logarithm), we can determine the value.
However, the options given are:
- 18
- \( \frac{1}{8} \)
- 0
- 8
- 1
None appear to directly correspond to \( \log 81 \) unless we're considering a specific logarithm base that relates to the numerical value.
If we evaluate \( 4 \cdot \log 3 \) using common logarithm:
Using \( \log 3 \approx 0.477 \):
\[ 4 \cdot \log 3 \approx 4 \cdot 0.477 \approx 1.908 \]
Among the provided options, inching closer to \( \log 81 \) of \( \log(3^4) = 4 \cdot \log 3 \approx 1.9 \), the nearest integer option is:
- 1 (since 1 is the closest whole number to about 1.9).
So, the choice that best fits is 1.