Question

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

• A. $3,-1$
• B. $3,1$
• C. $-3,-1$
• D. $-3,1$

Answer 1

The correct option is A $3,-1$

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

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

$\Rightarrow 2^{x^2}={8.2}^{2x}$

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

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

$\Rightarrow x^2=2x+3$ ....As bases are equal, powers must be equal

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

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

$\therefore x=3,-1$