Hi I have two questions here, which I do not know how to prove.

1.) Prove that (lnx)/x ≤ 1/e for all x>0.

I know to find the maximum value of (lnx)/x, I got x=e. But then what do I do? I subbed x=e back into (lnx)/x and I got 1/e.. 1/e ≤ 1/e doesn't make sense..

2.) Prove that lnx ≤ x-1 for all x>0.

Do I find the maximum value for lnx? I can't really get the maximum value for I'll get 1 = 0.

Please help, thank you so so much!