$x^{x}$ = $e^{\frac{1}{e}}$

I used desmos calculator and put in the functions $x^{x}$ and y= $e^{\frac{1}{e}}$ , and I want to know what the exact input is for x to get $e^{\frac{1}{e}}$ . I do know it's about 1.3211.

The problem for me is that I can't get x by itself without there being another x on the other side of the equation.

#Algebra

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

Hint: Lambert-W function is useful in solving such problem if you want to approach this problem without the use of calculator.

Michael Huang - 3 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

xxx^{x}xx=e1ee^{\frac{1}{e}}ee1​

Comments

$x^{x}$ = $e^{\frac{1}{e}}$