The following can't be true, but I can't discover my error. Can anyone see it?

$
\frac{i \pi n}{x}=\ln(-1^{\frac{n}{x}})=\ln(-1)+\ln(1^{\frac{n}{x}})=i\pi
$

(n is a positive integer and x is a positive real number)

Thanks

2. Don't you think this is a topic for university math help?^^

3. Originally Posted by rainer
The following can't be true, but I can't discover my error. Can anyone see it?

$
\frac{i \pi n}{x}=\ln(-1^{\frac{n}{x}})=\ln(-1)+\ln(1^{\frac{n}{x}})=i\pi
$

(n is a positive integer and x is a positive real number)

Thanks
$(-1)^{\frac{n}{x}}=(-1)(-1)....(-1)$ for $\frac{n}{x}$ times

or $\left(\sqrt{-1}\right)^{\frac{2n}{x}}$

Using the laws of logs.. $log(ab)=loga+logb$

but you cannot split $(-1)^{\frac{n}{x}$ into $(-1)(1)^{\frac{n}{x}}$