Number of Solution of equation {(x)^{x√ x }} = {(x√ x )^x} are

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Basic of Logarithms

easy

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

A

$4.5$

B

$1$

C

$-1$

D

$0$

Solution

(b) ${x^{x\sqrt x }} = {(x\sqrt x )^x} \Rightarrow {x^{{x^{3/2}}}} = {({x^{3/2}})^x}$

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

$ \Rightarrow $${x^{3/2}} = {3 \over 2}x$ $ \Rightarrow $${x^{1/2}} = {3 \over 2}$

$ \Rightarrow $$x = {9 \over 4}$

Also $x = 1$ is an obvious solution.

Standard 11

Mathematics

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