Proof of limit derivation of Natural Logrithm

[cmcraes]

The natural logarithm can be expressed as
lim n(x^(1/n)−1)
n->ifinity

Can someone please derive this for me? I've tried using the limit definition of e^x and then applying f^-1(x) but i can only get
((n*x)-1)^1/n

any help is greatly appreciated thanks!

 

[tiny-tim]

hi cmcraes!

(try using the X² button just above the Reply box )

x = e^logx ? ​

 

[cmcraes]

No that doesn't use limits nor does it prove anything other than the fact that the natural log and the exponential function cancel each other out

ps: I am on mobile so its not easy to do math print

 

[tiny-tim]

expand e^logx/n