x-x-x-x-find-x-

Question Number 175554 by Linton last updated on 02/Sep/22

x^{\sqrt{x}} = \sqrt{x^{x}}

f i n d x

Answered by mr W last updated on 02/Sep/22

x = 0

x^{x^{\frac{1}{2}} - \frac{x}{2}} = 1

\Rightarrow x = 1

\Rightarrow x^{\frac{1}{2}} - \frac{x}{2} = 0 \Rightarrow x = 4

Commented by BaliramKumar last updated on 02/Sep/22

x = 0 undefiend

Commented by mr W last updated on 02/Sep/22

u n d e f i n e d f o r y o u, b u t n o t f o r a l l!

Commented by mr W last updated on 02/Sep/22

Commented by BaliramKumar last updated on 02/Sep/22

y o u a r e r i g h t s i r

3 s o l u t i o n v a l i d

Commented by BaliramKumar last updated on 02/Sep/22

x^{\sqrt{x}} = \sqrt{x^{x}}

x^{x^{\frac{1}{2}}} = x^{\frac{x}{2}}

x^{\frac{1}{2}} l o g (x) = \frac{x}{2} l o g (x)

l o g (x) {\sqrt{x} - \frac{x}{2}} = 0

l o g (x) {2 \sqrt{x} - x} = 0

l o g (x) {2 - \sqrt{x}} \sqrt{x} = 0

\log_{e} (x) = 0 2 - \sqrt{x} = 0 \sqrt{x} = 0

x = e^{0} \sqrt{x} = 2 x = 0

x = 1 x = 4 x = 0

Commented by BaliramKumar last updated on 02/Sep/22

Answered by Rasheed.Sindhi last updated on 02/Sep/22

x^{\sqrt{x}} = \sqrt{x^{x}}

x^{x^{1 / 2}} = x^{x / 2}

x^{1 / 2} = x / 2

x^{1 / 2 - 1} = 1 / 2

\frac{1}{x^{1 / 2}} = \frac{1}{2}

x^{1 / 2} = 2

x = 2^{2} = 4