Maximum value of (log x) / x

Y = log x / x

y ' = ((log x) ' * x - (x) ' * log x) / x²=

= (1/x * x - 1 * log x) / x² =

= (1 - log x) / x²

y ' = 0;

1 - log x = 0

log x = 1

x = e

The maximum value:

y max = log e / e = 1 / e