Question

Solution of the equation $(x{)}^{x\sqrt{x}}=(x\sqrt{x}{)}^x$ is

• A. $\frac{9}{4}$
• B. $1$
• C. $-1$
• D. $0.5$

Answer 1

The correct option is A $\frac{9}{4}$

$(x{)}^{x^{3/2}}=(x^{3/2}{)}^x$

$(x{)}^{x^{3/2}}=(x{)}^{3x/2}$

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

$x\sqrt{x}-\frac{3x}{2}=0$

$x[\sqrt{x}-\frac{3}{2}]=0$

$\sqrt{x}=\frac{3}{2}$

$x={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$

Among the options available $A$ is appropriate.