To solve the given expression involving logarithms, we will use the properties of logarithms to simplify it:
1. The initial expression is:
[tex]\[
\log \frac{14}{3} + \log \frac{11}{5} - \log \frac{22}{15}
\][/tex]
2. Use the property of logarithms that states [tex]\(\log a + \log b = \log (a \cdot b)\)[/tex]:
[tex]\[
\log \left( \frac{14}{3} \cdot \frac{11}{5} \right) - \log \frac{22}{15}
\][/tex]
3. Multiply the fractions inside the logarithm:
[tex]\[
\frac{14}{3} \cdot \frac{11}{5} = \frac{14 \cdot 11}{3 \cdot 5} = \frac{154}{15}
\][/tex]
4. Substitute back into the expression:
[tex]\[
\log \frac{154}{15} - \log \frac{22}{15}
\][/tex]
5. Use the property [tex]\(\log a - \log b = \log \left( \frac{a}{b} \right)\)[/tex]:
[tex]\[
\log \left( \frac{\frac{154}{15}}{\frac{22}{15}} \right)
\][/tex]
6. Simplify the fraction inside the logarithm:
[tex]\[
\frac{\frac{154}{15}}{\frac{22}{15}} = \frac{154}{15} \cdot \frac{15}{22} = \frac{154}{22} = 7
\][/tex]
7. Substitute back into the expression:
[tex]\[
\log 7
\][/tex]
Thus, the correct answer is:
[tex]\[
\log 7
\][/tex]
