type the correct answer in the box. $log \frac{14}{3} + log \frac{11}{5} - log \frac{22}{15} = log square$

Explanation:

Step1: Combine logs via product rule

$\log \frac{14}{3} + \log \frac{11}{5} = \log\left(\frac{14}{3} \times \frac{11}{5}\right)$

Step2: Simplify the product inside log

$\log\left(\frac{14 \times 11}{3 \times 5}\right) = \log\left(\frac{154}{15}\right)$

Step3: Combine with subtraction via quotient rule

$\log\left(\frac{154}{15}\right) - \log \frac{22}{15} = \log\left(\frac{154}{15} \div \frac{22}{15}\right)$

Step4: Simplify the division inside log

$\log\left(\frac{154}{15} \times \frac{15}{22}\right) = \log\left(\frac{154}{22}\right) = \log 7$

Answer:

7