Question

What are possible values of x if `ln(x-4) +ln(3) <=0`?

Answer 1

Possible values of `x` are given by `4< x<=13/3`

Explanation:

We can write `ln(x-4)+ln3<=0` as

`ln(3(x-4))<=0`

graph{lnx [-10, 10, -5, 5]}

Now as `lnx` is a function which always increases as `x` increases (graph shown above) as also that `ln1=0`, this means

`3(x-4)<=1`

i.e. `3x<=13`

and `x<=13/3`

Observe that as we have `ln(x-4)` domain of `x` is `x>4`

Hence possible values of `x` are given by `4< x<=13/3`