See the power rule

$$ \frac {x^a} {x^b} =x^{E_1-E_2} $$

$log_a \frac {x^c} {x^y}=> a^?=\frac {x^c} {x^y}$

$log_a(x^c)$$-log_a(x^y)=?$

Remember

$log_a(x-y) is a^?=x-y$

$log_a(\frac {a^n} {a^v})$ is not $\frac {log_a(a^n)} {log_a(a^v)}$

$log_4(\frac {16} {1})$ is not $\frac {log_4(16)} {log_4(1)}$