Question

${(lnx)}^{2}$
☝This equal to which one of them
Which one of them is the right wrting of that☝?​

Answer 1

I think the best way to remove all ambiguity is to write

$\bigg(\ln(x)\bigg)^2$

$\ln^2(x)$ is often used to mean the same thing, but in some contexts it is used to mean the composition of logarithms, $\ln^2(x) := \ln(\ln(x))$.

$\ln x^2$ and $\ln(x^2)$ and $\ln(x)^2$ could all mean the same thing - the logarithm of the quantity $x^2$. For real, non-zero $x$, this is equivalent to $\ln(x^2) = 2\ln|x|$, but this is not true for either of the squared- or compound-logarithm interpretations.

$\bigg(\ln(x)\bigg)^2$ very clearly shows what's being squared