Multiple weak light bulbs vs one strong light bulb
You have a number of issues affecting the poor lighting in the mirror. When light hits you when facing the mirror it's reflected light coming off the ceilings, walls and other items in the room.

The intensity of light falls off exponentially following the inverse square rule. When you double the distance the intensity of light is 1/4th. Triple the distance it's 1/9th as strong. 

The closer you are to the light source the more intense the light will be. Reflected light not only loses intensity because your walls aren't mirrors but because it also has a greater distance until it reaches you.

More lights provide more even illumination and you can theoretically get away with much lower total lumens than if you used a single bulb.

Edit: Here are some more details to illustrate the point. Assume you have a 10'x10' room currently illuminated with 1 light source in the center of the room. You want to replace that single fixture with 4 lights instead. Each at 1/4 the power of the first light.



We start with 1 light with a power of 1 unit that is 60" away from the mirror and delivers a light intensity of 1 at the mirror. 

We replace it with 4 lights that are each 1/4 the power of the first unit. Two lights are about 42.426407" away from the mirror and two lights are 94.875" away.

The intensity of the closer lights are:
(60/42.426407)^2 * 0.25 (for reduced wattage) = ~0.5 
Half of the original intensity

The intensity of the 2 lights furthest away is
(60/94.875)^2 * 0.25 = ~0.1 of the original intensity.

Add up the 4 lights:
0.5 + 0.5 + 0.01 + 0.01 = 1.2

So you're getting roughtly 20% more direct light than you were with the one bulb. With the given placement you're also not blocking the light by standing between the light and the mirror.