ln (2 + x^2) = x: How do you solve this?

[ku1005]

Hey guys, just wondeirng how you would go about solving the following, because im really quite stumpted?

Q)does there exist a positive real number satisfying

ln (2 + x^2) = x

Justify your answer

I have simply :

e^x = 2 + 2x

where the right hand side is a line intecepting the y axis at 2 and the e^x intercepts the y axcis at one and then proceeds upwards, therefore , in my head i can see yes there is a value, but im unsure how to solve it??

cheers for any tips!

 

[pka]

Re: Hw do you solve this???

Q)does there exist a positive real number satisfying
ln (2 + x^2) = x
e^x = 2 + 2x

Did you graph those last two expressions? If it is clear thy are equal at approx. x=3.
If you know Newton’s method, you can apply it to this function:
\(\displaystyle f(x) = e^x - 2x -2\) with first guess x=3.

 

[ku1005]

no i didnt graph them, not aloud to use graphics calculators in my maths classes, but yeah, forgot about newtons method being helpful here, thanks.