Question

Solve for value of $x$ $3^{x^2}:3^x=9:1$

Answer 1

Given equation is $3^{x^2}:3^x=9:1$

$=>\frac{3^{x^2}}{3^x}=\frac{3^2}{1}$

By using law $a^m÷a^n=a^{m-n}$

$=>3^{x^2-x}=3^2$

As base is same, we can equate the powers,

$\Rightarrow x^2-x=2$

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

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

$\Rightarrow x(x-2)+(x-2)=0$

$\Rightarrow (x-2)(x+1)=0$

$\Rightarrow x=2$ or $x=-1$

$\Rightarrow x=2$ satisfies the condition.