If $${x^{x\sqrt x }} = {\left( {x\sqrt x } \right)^x}{\text{,}}$$ then x equals to?
A. $$\frac{4}{9}$$
B. $$\frac{2}{3}$$
C. $$\frac{9}{4}$$
D. $$\frac{3}{2}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {x^{x\sqrt x }} = {\left( {x\sqrt x } \right)^x} \cr & {x^{x\sqrt x }} = {\left( {{x^{\frac{3}{2}}}} \right)^x} \cr & {x^{x\sqrt x }} = {x^{\frac{3}{2}x}} \cr} $$(If bases are same then their power is also same)
$$\eqalign{ & \therefore x\sqrt x = \frac{3}{2}x \cr & \Rightarrow \sqrt x = \frac{3}{2} \cr & \Rightarrow x = {\left( {\frac{3}{2}} \right)^2} \cr & \Rightarrow x = \frac{9}{4} \cr} $$
Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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