Solve Product of Logarithms: log₄(9) × log₁₃(7) Evaluation

$\log_49\times\log_{13}7=$

To solve the problem $\log_49 \times \log_{13}7$, we'll employ the change of base formula for logarithms:

• Step 1: Apply the change of base formula to each logarithm.
• Step 2: Use logarithm properties and analyze transformations for a match with choices.

Now, let's work through each step:
Step 1: Use the change of base formula on each log:
$\log_49 = \frac{\log_a 9}{\log_a 4}$ and $\log_{13}7 = \frac{\log_b 7}{\log_b 13}$, where $a$ and $b$ are arbitrary positive bases.
Both expressions use a common base not relevant for the solution but illustrate the transformation ability.

Step 2: We'll recombine and look for products that can utilize these, such as:

$\log_{13}9\times\log_47$ becomes $\frac{\log_a 9}{\log_a 13} \times \frac{\log_b 7}{\log_b 4}$
Applying cross multiplication or iteration forms, the structure aligns with the multiplication identity for this problem due to independence of base.

Therefore, the transformed expression satisfying the criteria is $\log_{13}9\times\log_47$.