Question

Question #984b4

Answer 1

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

Explanation:

`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.