Question

# 50 points


prove ...


$x {}^{ \sqrt{x} } = \sqrt{x {}^{x} }$
​

Answer 1

$lhs \\ {x}^{ \sqrt{x} } \\ taking \: log \: \\ \sqrt{x }log( {x} ) \\ \\ rhs \\ \sqrt{ {x}^{x} } \\ {x}^{ \sqrt{x} } \\ taking \: log \\ \sqrt{x} log(x)$

$hence \: lhs \: = rhs = \sqrt{x} log(x) proved$

Answer 2

Answer:

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