Moisture issue in bathroom
Exhaust fans installed in older homes that have not been upgraded are often undersized. Check your existing unit to ensure it complies with the following advice from a major exhaust fan manufacturer:


  A good general rule for bathrooms with 8’ ceiling heights is to allow at least 1 cubic foot per minute (CFM) of ventilation for every square foot of room size for bathrooms under 100 square feet.For larger rooms, the recommendation is based on adding 50 CFM for each toilet, bathtub or shower and 100 CFM for jetted tubs. 


You can usually find a sticker or placard with model # and rating on the housing, if you remove the fan grill/cover.

If it does not meet the quoted spec consider an upgrade. Also make sure your existing unit is properly ducted to the outside of your home and that the duct is not pinched or blocked.