1. A topical pharmaceutical composition for lightening skin comprising an effective amount of a compound of formula I: wherein X is hydrogen; halogen; (C1-C6)alkyl; OR<1> or NHR<1> wherein R<1> represents hydrogen; n is 0 to 3; and the dashed line represents an optional double bond; or a pharmaceutically acceptable salt thereof, and a pharmaceutically acceptable carrier. 2. The topical pharmaceutical composition of claim 1, which is in the form of a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 3. The topical pharmaceutical composition of claim 1, which is in the form of a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 4. The topical pharmaceutical composition of claim 1, wherein the compound of formula I is 4-cyclohexylresorcinol. 5. The topical pharmaceutical composition of claim 4, which is in the form of a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 6. The topical pharmaceutical composition of claim 4, which is in the form of a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 7. The topical pharmaceutical composition of claim 1, wherein the compound of formula I is 4-cyclopentylresorcinol. 8. The topical pharmaceutical composition of claim 7, which is in the form of a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 9. The topical pharmaceutical composition of claim 7, which is in the form of a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 10. The topical pharmaceutical composition of claim 1, which further comprises a sunscreen. 11. The topical pharmaceutical composition of claim 1, which further comprises resveratrol or another active agent that is an anti-oxidant. 12. The topical pharmaceutical composition of claim 1, which further comprises retinoic acid or a derivative of retinoic acid or a compound which reacts with retinoic acid receptors for stipulating or increasing the composition abilities effective for lightening skin or reducing the pigmentation of skin in a human. 13. The topical pharmaceutical composition of claim 1, which further comprises glycolic acid, trichloroacetic acid or another skin peeling agent. 14. The topical pharmaceutical composition of claim 1, wherein a compound of the formula I or a pharmaceutical salt thereof, which is effective for lightening skin or reducing the pigmentation of skin in a human, is a tyrosinase-inhibiting effective amount. 15. Use the compound of the formula I wherein X is hydrogen; halogen; (C1-C6)alkyl; OR<1> or NHR<1> wherein R<1> represents hydrogen; n is 0 to 3; and the dashed line represents an optional double bond; or a pharmaceutically acceptable salt thereof, and a pharmaceutically acceptable carrier for producing a medicament effective for lightening skin or reducing the pigmentation of skin in a human. 16. Use of claim 15, wherein the compound of the formula I or a pharmaceutically acceptable salt thereof is formulated in a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 17. Use of claim 15, wherein the compound of formula I or pharmaceutically acceptable salt thereof is formulated in a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 18. Use of claim 15, wherein the compound of formula I or pharmaceutically acceptable salt thereof is 4-cyclohexylresorcinol. 19. Use of claim 18, wherein the compound of the formula I or a pharmaceutically acceptable salt thereof is formulated in a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 20. Use of claim 18, wherein the compound of formula I or pharmaceutically acceptable salt thereof is formulated in a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 21. Use of claim 15, wherein the compound of formula I or pharmaceutically acceptable salt thereof is 4-cyclopentylresorcinol. 22. Use of claim 21, wherein the compound of the formula I or a pharmaceutically acceptable salt thereof is formulated in a water-alcohol solution, an oil-in-water emulsion, a water-in-oil emulsion, an emulsified gel, or a two-phase system. 23. Use of claim 21, wherein the compound of formula I or pharmaceutically acceptable salt thereof is formulated in a lotion, cream, milk, gel, jelly, paste, ointment, salve, mask, microspheres, nanospheres, or vesicular dispersion. 24. Use of claim 15, wherein the medicament further comprises retinoic acid or a derivative of retinoic acid or a compound which reacts with retinoic acid receptors for stipulating or increasing the composition abilities effective for lightening skin or reducing the pigmentation of skin in a human.