1. ## Notation of solution

ln(x)(sin(x)) = 0
for x= 0, Pi, 2Pi etc... and for 1
how do you write this correctly with the correct symbols and terms?

2. Originally Posted by Schdero
ln(x)(sin(x)) = 0
for x= 0, Pi, 2Pi etc... and for 1
how do you write this correctly with the correct symbols and terms?
Write it as

$x = \left\{1, \pi n\right\}$, where $n \in \mathbf{Z}$.

3. Originally Posted by Schdero
ln(x)(sin(x)) = 0
for x= 0, Pi, 2Pi etc... and for 1
how do you write this correctly with the correct symbols and terms?
Notice that any value in the range $x\le0$ is actually not a solution because $\ln x$ will be undefined in that region.

So the solution should be
$1,~k\pi$ where k is a natural number
or, if you want to be precise (this is not usually necessary unless you are in advanced math courses where you've learned set theory), you should use set notation, i.e.,
$x \in \{1\} \cup \{k\pi:k\in\mathbb{N}\}$