The expression given in the image is:

$^2\log 7 \times ^3\log 16 \times ^7\log 9 = \dots$

This uses an unconventional notation for logarithms with superscripts. Generally, superscripts on logarithms suggest a change of base. The standard way to interpret this notation is as follows:

• $^2\log 7$ means the logarithm of 7 with base 2, i.e., $\log_2 7$
• $^3\log 16$ means the logarithm of 16 with base 3, i.e., $\log_3 16$
• $^7\log 9$ means the logarithm of 9 with base 7, i.e., $\log_7 9$

Thus, the expression becomes:

$\log_2 7 \times \log_3 16 \times \log_7 9$

Step-by-step breakdown:

1. Evaluate $\log_2 7$: This is the logarithm of 7 in base 2. Using a calculator: $\log_2 7 \approx 2.807$

2. Evaluate $\log_3 16$: This is the logarithm of 16 in base 3: $\log_3 16 \approx 2.523$

3. Evaluate $\log_7 9$: This is the logarithm of 9 in base 7: $\log_7 9 \approx 1.129$

4. Multiply the results: Now, we multiply these values: $2.807 \times 2.523 \times 1.129$

Let me compute that for you.The result of the expression $\log_2 7 \times \log_3 16 \times \log_7 9$ is approximately $7.996$.

Would you like more details or have any questions about this solution?

Here are five related questions to expand your understanding:

1. How can you convert a logarithm from one base to another?
2. What is the change of base formula for logarithms?
3. What are some real-world applications of logarithms?
4. How do logarithmic and exponential functions relate to each other?
5. Can you explain why logarithms with different bases can still be multiplied?

Tip: When calculating logarithms with unconventional bases, you can use the change of base formula, $\log_b x = \frac{\log_c x}{\log_c b}$, where $c$ is any base (often base 10 or base $e$ is used).