They combined two rules. First, they converted the exponent to a coefficient, like you were going to do. Then, they used the rule . Multiplication by 1 doesn't change anything so you are left with just the coefficient.
Original problem is . Ive gotten it to . Ordinarily I would change the 3x+5 into the coefficient of lne and go from there but in the example problem Im looking at they simply remove the ln e. Basically this is what they did: They took and simplified it to . So my question is what rule or property did they use to get rid of the LN e?