To evaluate \(\log_2 843\), we can start by rewriting the logarithm in terms of base 10 or using properties of logarithms if necessary. However, we can determine values without doing extensive calculations.
Let's look at the responses provided:
- 643
- \(\frac{64}{3}\)
- 163
- \(\frac{16}{3}\)
- 4
- 94
To find out which of these is equal to \(\log_2 843\), we can approach this by estimating or calculating values of \(2^x\) for the values suggested.
Since we know \(2^{10} = 1024\) and \(2^9 = 512\), we can estimate that \(\log_2 843\) should be around between 9 and 10.
Now evaluating choices:
- \(643\) - Corresponds to a logarithm value much greater than 10. Not plausible.
- \(\frac{64}{3} \approx 21.33\) - Clearly larger than 10.
- \(163\) - Also much larger than 10.
- \(\frac{16}{3} \approx 5.33\) - This value is less than 9, not plausible.
- \(4\) - Far too low and corresponds to \(\log_2 16\) which is 4.
- \(94\) - Again, much less than 10.
Since none appear to be close to what we expect of \(\log_2 843\) (which is around 9.4), the only reasonable estimate based on the logarithmic scale and the rough values derived is:
None of the provided options accurately reflects \(\log_2 843\).
If you are constrained to choose an option, the value \(\frac{16}{3}\) (approx 5.33) is likely the least incorrect but not very close due to it being below the expected value. If accurate options for \(\log_2 843\) are needed, none from your list suffice.