ANSWER
[tex]log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7[/tex]
EXPLANATION
The given logarithmic expression is:
[tex] log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We apply the product rule to the first two terms to get:
[tex]log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We the apply the quotient rule:
[tex]log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} ) [/tex]
[tex]log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} ) [/tex]
We cancel out the common factors and simplify to obtain:
[tex]log( 7 ) [/tex]
