Question

Solve:$2^{x^2}:2^{2x}=8:1$

Answer 1

$2^{x^2}:2^{2x}=8:1$

$\frac{2^{x^2}}{2^{2x}}=\frac{8}{1}$

We know that, $\frac{a^m}{a^n}=a^{m-n}$

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

Since bases are same we can equate the powers.

$\Rightarrow x^2-2x=3$

$\Rightarrow x^2-2x-3=0$

$\Rightarrow x^2-3x+x-3=0$

$\Rightarrow x(x-3)+(x-3)=0$

$\Rightarrow (x-3)(x+1)=0$

$\Rightarrow x=3,-1$