Do you mean:

lim(x->-inf) (e^x)[ln(|x|) + 3x]

or:

lim(x->-inf) exp(x [ln(|x|)+3x])

The first of these goes to 0, as e^x decreases faster than |x|^k for

and real k as x -> -inf.

The second of these goes to +inf, as for large |x| x (ln(|x|+3x)

behaves like x^2.

If need be all of this can be made rigourous.

RonL