Question

How do you find the Limit of `ln (x)/ln (3x)` as x approaches infinity?

Answer 1

`1`

Explanation:

`lim_(x to oo) ln (x)/ln (3x)`

`lim_(x to oo) ln (x)/(ln 3 + ln x )`

`lim_(x to oo) 1/(ln 3/ (ln x ) + 1 )`

`(lim_(x to oo) 1)/(lim_(x to oo) ln 3/ (ln x ) + 1 )`

`= 1/1 = 1` as `lim_(x to oo) ln (x) = oo`