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

Explanation:

Step1: Use log addition rule

According to the rule $\log a+\log b=\log(ab)$, we have $\log\frac{14}{3}+\log\frac{11}{5}=\log(\frac{14}{3}\times\frac{11}{5})=\log\frac{154}{15}$.

Step2: Use log subtraction rule

According to the rule $\log a - \log b=\log\frac{a}{b}$, we get $\log\frac{154}{15}-\log\frac{22}{15}=\log\frac{\frac{154}{15}}{\frac{22}{15}}$.

Step3: Simplify the fraction

$\frac{\frac{154}{15}}{\frac{22}{15}}=\frac{154}{15}\times\frac{15}{22}=7$.

Answer:

$7$