To find the value of \( \log 81 \), we first rewrite 81 as a power of 3:
\[ 81 = 3^4 \]
Using the properties of logarithms, particularly \( \log_b(a^c) = c \cdot \log_b(a) \), we can express \( \log 81 \) as:
\[ \log 81 = \log(3^4) = 4 \cdot \log 3 \]
However, without knowing the base of the logarithm or the numerical value of \( \log 3 \), we can't determine a specific numerical value for \( \log 81 \).
Assuming the problem is asking for a specific output from the given choices, we will provide an answer based on the conventional logarithm (base 10) calculation:
While we know \( \log 81 = 4 \cdot \log 3 \), to match it with the provided responses, one might deduce that the most reasonable output given your alternatives could be suggested, but typically, \( \log 81 \) is not directly equal to any standard value among those options.
Among the choices:
- 1
- 0
- 18
- \( \frac{1}{8} \)
- 8
None directly corresponds to a standard value for logarithms as calculated above under common bases.
If the logarithm was calculated based on base 3, we would get:
- For base 3, \( \log_3(81) = 4 \).
However, if we treat the responses simply as needing to match a simplified answer, \( 1 \) usually aligns with the logarithm of a value close to its own base.
It seems like there may be an error or lack of clarity in the choices presented since typical logarithmic calculations do not strictly provide solutions aligning to these whole or fractional numeric values without context. Can you confirm the context in which the logarithm is computed or any specific base intended?