Finding the 'x'

How can we solve these type of problems:

e.g. $2^{x}=x$

or, $2^{x}=x^{2}$

To find the possible value(s) of x.

#Algebra

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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}`	$\boxed{123}$

Comments

use log in both this is the simplest way 1st one answer is no solution 2nd one has 2 solution I.e., 2&4

Abhishek Sharma - 5 years, 7 months ago

thanks...

Dinesh Nath Goswami - 5 years, 7 months ago

actually it has 3 solutions

Jun Arro Estrella - 5 years, 7 months ago

Try using graphs and apply calculus.

Deepak Kumar - 5 years, 8 months ago

thanks. I'll try that way.

Dinesh Nath Goswami - 5 years, 8 months ago

Use logarithm too. That will make the problem easier.

Sachin Vishwakarma - 5 years, 8 months ago

@Sachin Vishwakarma – thanks...

Dinesh Nath Goswami - 5 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}`	$\boxed{123}$