To solve for \( \log_2 843 \), we can first convert it to a more manageable form using properties of logarithms, but let's check the options given in the context of logarithms.
The options provided seem to be numeric, but to evaluate them properly:
- 643
- \( \frac{64}{3} \)
- 163
- \( \frac{16}{3} \)
- 4
- 94
None of these options is a direct form of logarithmic values. Hence, we need to assess if any of these answers equal \( \log_2 843 \) through calculating or estimating \( \log_2 843 \).
Since \( 843 \) is between \( 512 (2^9) \) and \( 1024 (2^{10}) \):
\[ 9 < \log_2 843 < 10 \]
Now, let's approximate \( \log_2 843 \) using the change of base formula:
\[ \log_2 843 = \frac{\log_{10} 843}{\log_{10} 2} \]
We can calculate \( \log_{10} 843 \approx 2.926 \) and \( \log_{10} 2 \approx 0.301 \):
\[ \log_2 843 \approx \frac{2.926}{0.301} \approx 9.71 \]
This approximation suggests \( \log_2 843 \) is around 9.71, which is not directly equal to any provided responses but demonstrates where it falls numerically.
Among the options, 4 and 94 are clearly less than and greater than our approximated value.
Given that the value does not cleanly map to any listed responses, make sure to clarify whether alternative values must be selected, or if \( \log_2 843 \) equal to another form?
But seeing closely given responses, none accurately represent \( \log_2 843 \). However, it looks like a decimal/fractional response is likely as it is not equal to any integer outcomes 4 or 94.
If forced to choose based on the closest numerical fall, \( \frac{64}{3} \approx 21.33 \)—also isn't logically close given expected outcomes.
The more reasonable decision could likely be:
None of the suggested choices directly equal \( \log_2 843 \).