There is more to the design than simply sizing the beam, there are connection details and an analysis of the flex of the beam that should also be done at the same time the beam is evaluated for strength. Any structural engineer worth a nickel can tell you based upon an inspection of your site and a review of the loading what size beam you need, or in your case how much you can span with a specific size beam. If none of this makes any sense, let me make it a little simpler. Deflection is related to the fourth power of the span length, while maximum fiber bending stress is related to the square of the length, so neither factor scales directly with the beam moment of inertia. Maximum span is governed by the more restrictive of the deflection of the beam at the center, or the bending strength of the beam. The allowable span for a beam is governed by the moment of inertia of the beam (depends on the size of the beam), the maximum allowable fiber bending stress (depends on the type of wood and the grade), the modulus of elasticity of the material (depends on the species of wood), and the loading (dead plus live load, often governed by code).
No, you cannot multiply the length by 1.5.
