To evaluate $\log_2\left(\frac{9}{14}\right)$, follow these steps:

1. Use the logarithmic property:
   $\log_b\left(\frac{a}{c}\right) = \log_b(a) - \log_b(c)$ This gives: $\log_2\left(\frac{9}{14}\right) = \log_2(9) - \log_2(14)$

2. We now need to approximate $\log_2(9)$ and $\log_2(14)$:

   • $\log_2(9) \approx 3.1699$
   • $\log_2(14) \approx 3.8074$

3. Subtract the two values: $\log_2\left(\frac{9}{14}\right) = 3.1699 - 3.8074 = -0.6375$

So, $\log_2\left(\frac{9}{14}\right) \approx -0.6375$.

Would you like more details on logarithmic properties, or any clarifications?

Here are 5 related questions:

1. How would you evaluate $\log_2(14)$ using the change of base formula?
2. What is the value of $\log_2\left(\frac{14}{9}\right)$?
3. How do you convert between different logarithmic bases?
4. What are common logarithmic identities?
5. How do you approximate logarithmic values without a calculator?

Tip: Using the change of base formula, $\log_b(x) = \frac{\log(x)}{\log(b)}$, can help you compute logs with different bases more easily.