A telescope is limited  in its usefulness by the brightness of the star that it is aimed  at and by the diameter of its lens. One measure of a star's brightness is its magnitude; the dimmer the star, the larger its magnitude. A formula for the limiting magnitude L of a telescope, that is, the magnitude of the dimmest star that it can be used to view, is given by

L = 9 + 5.1 log d

where d is the diameter (in inches) of the lens.

(a) What is the limiting magnitude of a 3.5-inch telescope?

(b) What diameter is required to view a star of magnitude 14?