If f'(x) = 2/x and f(sqrt of e) =5, then f(e) =?

Question

anonymous · Answer

$$f(\sqrt{e})=5$$??

anonymous · Answer

are you allowed to integrate? if so, then if 
$$f'(x)=\frac{2}{x}$$ then 
$$f(x)=2\ln(x)+C$$

anonymous · Answer

we can find C easily enough, since 
$$f(e)=5=2\ln(e)+C=2+C$$ making $C=3$ and so your funciton is 
$$f(x)=2\ln(x)+3$$

anonymous · Answer

Then u plug in e right? But u get 2ln (e) +3 which is 5 but in teh answer key it says its 6

anonymous · Answer

oh because i am an idiot

anonymous · Answer

it says 
$$f(\sqrt{e})=5$$

anonymous · Answer

so we have 
$$f(x)=2\ln(x)+C$$ and we know that 
$$f(\sqrt{e})+C=5$$ so 
$$2\ln(\sqrt{e})+C=5$$
$$1+C=5$$ and so 
$$C=4$$

anonymous · Answer

therefore your function is 
$$f(x)=2\ln(x)+4$$ and then of course 
$$f(e)=2\ln(e)+4=2+4=6$$
sorry about my original mistake

anonymous · Answer

OH no problem! Thanks for finxing it! =)