# The intersection of x and ln(x)^p, where p>1

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• Nov 24th 2009, 05:20 AM
Guemo
The intersection of x and ln(x)^p, where p>1
I'm just wondering how I find this intersection,

$
x=(\ln(x)^p) \quad p>1
$

where x>2

I tried to take the logarithm of both sides but I'm not sure which step to take from that, or if that's the right step to begin with.
• Nov 24th 2009, 07:58 AM
Drexel28
Quote:

Originally Posted by Guemo
I'm just wondering how I find this intersection,

$
x=(\ln(x)^p) \quad p>1
$

where x>2

I tried to take the logarithm of both sides but I'm not sure which step to take from that, or if that's the right step to begin with.

I assume intersection (just making sure) means solve the equation $x=\ln^p(x)\quad p>1$. There isn't a closed form solution for this.
• Nov 24th 2009, 08:06 AM
Guemo
Ok, thank you, just wanted to be sure! Think I can manage from now :D