Help Needed: Explaining x^{x} = e^{xlgx} and x^{a}

[pamparana]

Hello,

I am having trouble getting my head around this:

Can someone explain why
x^{x} = e^{xlgx}

I cannot seem to understand why this is true. I am quite weak when it comes to handling exponentials. I dare say that I am terrified of e!

Also, would this also hold for a static power: so x^{a}

Thanks,

Luca

 

[rochfor1]

Remember that for a > 0, \ln ( a^b ) = b \ln a and the fact that exponentation and the natural logarithm are inverse functions.

 

[pamparana]

That makes sense!

Many thanks!