Question

If $3^{x-1}$ =9 and $4^{y+2}$ =64, what is the value of $\frac{x}{y}$

Answer 1

$3^{x-1}=9\Rightarrow 3^{x-1}=3^{2}Comparingthepowers,wegetx-1=2\Rightarrow x=2+1=3\therefore x=3and{4}^{y+2}=64\Rightarrow (4{)}^{y+2}=(4{)}^{3}Comparingthepowers,wegety+2=3\Rightarrow y=3-2=1\therefore y=1Now\frac{x}{y}=\frac{3}{1}=3$