ANSWER
[tex]log( {x}^{4} ) - log(x + 2)^{6} = log \frac{ {x}^{4} }{ {(x + 2)}^{6} } [/tex]
EXPLANATION
The given logarithmic function is
[tex]4 log(x) - 6 log(x + 2) [/tex]
Recall the power rule of logarithms.
[tex]n \log( {a}) = log( {a}^{n} ) [/tex]
We apply this rule to get:
[tex]log( {x}^{4} ) - log(x + 2)^{6} [/tex]
Recall the quotient rule:
We apply the quotient rule to get;
[tex] log(a) - log(b) = log( \frac{a}{b} ) [/tex]
[tex]log( {x}^{4} ) - log(x + 2)^{6} = log\frac{ {x}^{4} }{ {(x + 2)}^{6} } [/tex]
