The light intensity of a source is 100 candelas. the illuminance on a surface is 4 lux. how far is the surface from the source?

The answer is 5 meters.

The illuminance on a surface (E) is equal to the light intensity (I) divided by the square distance from the light source (d):
E = I ÷ d² [=] candela/ square meters = lux.
The unit of the illuminance is lux.

So, it is given:
E = 4 lux
I = 100 candelas
d = ?

If:
E = I ÷ d²
Then
d² = I ÷ E
⇒ d² = 100 ÷ 4
⇒ d² = 25

If we put both sides of the equation under the square root, then:
√d² = √25
⇒ d = 5 meters.

Therefore, the surface is 5 meters far from the light source.