Question
Solve for $x:9 \times 81^x=\frac{1}{27^{x-3}}$
✓
Answer
$9 \times 81^x=\frac{1}{27^{x-3}}$
$ \Rightarrow 3^2 \times 3^{4 x}=\frac{1}{3^3(x-3)}$
$\Rightarrow 3^2 \times 3^{4 x}=\frac{1}{3^{3 x-9}}$
$ \Rightarrow 3^2 \times 3^{4 x} \times 3^{3 x-9}=1 $
$ \Rightarrow 3^{2+4+3 x-9}=1 \times 3^0$
$\Rightarrow 2+4+3 x-9=0$
$ \Rightarrow 3 x-3=0 $
$ \Rightarrow x=1$
$ \Rightarrow 3^2 \times 3^{4 x}=\frac{1}{3^3(x-3)}$
$\Rightarrow 3^2 \times 3^{4 x}=\frac{1}{3^{3 x-9}}$
$ \Rightarrow 3^2 \times 3^{4 x} \times 3^{3 x-9}=1 $
$ \Rightarrow 3^{2+4+3 x-9}=1 \times 3^0$
$\Rightarrow 2+4+3 x-9=0$
$ \Rightarrow 3 x-3=0 $
$ \Rightarrow x=1$
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