Question
Solve for $x:5^{x2} : 5^x= 25 : 1$
✓
Answer
$5^{x 2}: 5^x=25: 1 $
$ \Rightarrow \frac{5 x^2}{5 x}=\frac{25}{1} $
$ \Rightarrow \frac{5 x^2}{5 x}=\frac{5^2}{1} $
$ \Rightarrow 5^{x 2}=5^2 \times 5^x $
$ \Rightarrow 5^{x 2}=5^{2+x} $
$ \Rightarrow x^2=2+x $
$ \Rightarrow x^2-x-2=0$
$\Rightarrow(x-2)(x+1)=0 $
$ \Rightarrow x-2=0$ or $x+1=0 $
$ \Rightarrow x=2$ or $x=-1 .$
$ \Rightarrow \frac{5 x^2}{5 x}=\frac{25}{1} $
$ \Rightarrow \frac{5 x^2}{5 x}=\frac{5^2}{1} $
$ \Rightarrow 5^{x 2}=5^2 \times 5^x $
$ \Rightarrow 5^{x 2}=5^{2+x} $
$ \Rightarrow x^2=2+x $
$ \Rightarrow x^2-x-2=0$
$\Rightarrow(x-2)(x+1)=0 $
$ \Rightarrow x-2=0$ or $x+1=0 $
$ \Rightarrow x=2$ or $x=-1 .$
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