Question #984b4

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Answer 1 · 2017-04-14T07:31:31

$x=sqrt(1/(e-1))$

$ln(1+x^2)=1+2ln x$

By Log Property: $rln x=ln x^r$ ,

$Rightarrow ln(1+x^2)=1+ln x^2$

By raising $e$ to both sides,

$Rightarrow e^(ln(1+x^2))=e^(1+ln x^2)=e^1 cdot e^(ln x^2)$

By Inverse Property: $e^(ln x)=x$ ,

$Rightarrow 1+x^2=ex^2$

By subtracting $x^2$ from both sides,

$Rightarrow 1=ex^2-x^2=(e-1)x^2$

By dividing both sides by $(e-1)$ ,

$Rightarrow 1/(e-1)=x^2$

By taking the square-root of both sides,

$pm sqrt(1/(e-1))=x$

Since the domain of $ln x$ is $x>0$ , we have

$x=sqrt(1/(e-1))$

I hope that this was clear.