Question

If ${27}^{x+1}=9^{x+3}=3^y$, find the respective values of $x$ and $y$.

• A. $3$ and $12$
• B. $12$ and $3$
• C. $6$ and $6$
• D. $4$ and $9$

Answer 1

The correct option is A $3$ and $12$

$Now{27}^{x+1}=9^{x+3}=3^y$

$Nowconsider,{27}^{x+1}=9^{x+3}$

$\to {27}^x.{27}^1=9^x.9^3$

$\to {27}^x.27=9^x.9^3$

$\to \frac{{27}^x}{9^x}=\frac{{\left(3^2\right)}^3}{3^3}$

$\to \frac{{\left(3^3\right)}^x}{{\left(3^2\right)}^x}=\frac{3^6}{3^3}$

$\to \frac{3^{3x}}{3^{2x}}=3^{6-3}$

$\to 3^{3x-2x}=3^3$

$\to 3^x=3^3$

$Comparingpower,wegetx=3.$

$Now{9}^{x+3}=3^y$

$\to 9^{3+3}=3^y$

$\to 9^6=3^y$

$\to {\left(3^2\right)}^6=3^y$

$\to 3^{12}=3^y$

$Comparingpower,wegety=12$