Question

\(\frac{9}{27^x}=\frac{3^{x+2}}{81}\)

Answer 1

=> 9.81 = 27.3^x+2

3².3⁴ = 3³.3^x.3²

3⁶ = 3^3+x.3²

3⁶:3² = 3^3+x

3⁴ = 3^3+x

<=> 3+x = 4

x = 4-3

x = 1

Answer 2

\(\frac{9}{27^x}=\frac{3^{x+2}}{81}\Rightarrow\frac{9}{27^x}=\frac{3^x.3^2}{9.9}\Rightarrow\frac{9}{27^x}=\frac{3^x.9}{9.9}\Rightarrow\frac{9}{27^x}=\frac{3^x}{9}\Rightarrow9.9=3^x.27^x\Rightarrow3^2.3^2=3^x.\left(3^3\right)^x\Rightarrow3^{2+2}=\left(3^{1+3}\right)^x\)

\(\Rightarrow3^4=\left(3^4\right)^x\Rightarrow x=1\)