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

English

Gujarati

Hindi

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

Share

Similar Questions

If ${({a^m})^n} = {a^{{m^n}}}$, then the value of $'m'$ in terms of $'n'$ is

easy

If $x = 3 – \sqrt {5,} $ then ${{\sqrt x } \over {\sqrt 2 + \sqrt {(3x – 2)} }} = $

hard

${{3\sqrt 2 } \over {\sqrt 6 + \sqrt 3 }} – {{4\sqrt 3 } \over {\sqrt 6 + \sqrt 2 }} + {{\sqrt 6 } \over {\sqrt 3 + \sqrt 2 }} = $

easy

Solution of the equation ${9^x} – {2^{x + {1 \over 2}}} = {2^{x + {3 \over 2}}} – {3^{2x – 1}}$

hard

${{12} \over {3 + \sqrt 5 – 2\sqrt 2 }} = $

medium