Question
Solve for $x:9 \times 3^x=(27)^{2 x-5}$
✓
Answer
$9 \times 3^x=(27)^{2 x-5} $
$ \Rightarrow 3^2 \times 3^x=\left(3^3\right)^{2 x-5} $
$ \Rightarrow 3^2 \times 3^x=3^{3 x \times^{(2 x-5)}}$
$ \Rightarrow 3^{2+x}=3^{6 x-15}$
$ \Rightarrow 1=\frac{3^{6 x-15}}{3^{2+x}} $
$ \Rightarrow 1=3^{6 x-15-2-x} $
$ \Rightarrow 3^0=3^{5 x-17}$
$ \Rightarrow 5 \times 17=0$
$ \Rightarrow x=\frac{17}{5} .$
$ \Rightarrow 3^2 \times 3^x=\left(3^3\right)^{2 x-5} $
$ \Rightarrow 3^2 \times 3^x=3^{3 x \times^{(2 x-5)}}$
$ \Rightarrow 3^{2+x}=3^{6 x-15}$
$ \Rightarrow 1=\frac{3^{6 x-15}}{3^{2+x}} $
$ \Rightarrow 1=3^{6 x-15-2-x} $
$ \Rightarrow 3^0=3^{5 x-17}$
$ \Rightarrow 5 \times 17=0$
$ \Rightarrow x=\frac{17}{5} .$
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