What is the domain of $arcsin(Ln(x))$ ?

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Answer 1 · 2016-08-04T10:37:22

Let $y=arcsin(lnx)$ hence $siny=lnx$

But the domain of $lnx$ is $x>0$

The domain of siny is $-1<=siny<=1$ hence

$-1<=lnx<=1$ hence $e^-1<=x<=e^1$

Finally the domain of $y=arcsin(lnx)$ is $D_y=[1/e,e]$

What is the domain of arcsin(Ln(x))arcsin(Ln(x))?