Question

Solve

$3^{x^2}:3^x=9:1$.

• A. $x=2,-1$
• B. $x=1,-1$
• C. $x=2,-2$
• D. $x=0,-1$

Answer 1

The correct option is A

$x=2,-1$

Given

$3^{x^2}:3^x=9:1$

$\Rightarrow$ $\frac{3^{x^2}}{3^x}=\frac{9}{1}$

$\Rightarrow$ $3^{x^2}=9\times 3^x$

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

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

Equating the powers

$x^2=2+x$

$x^2-x-2=0$

Solving this we get

$x=2,-1$