Logarithmic (and exponential) functions are widely used in describing economic and physical phenomenon such as compound interest, population growth, memory retention, decay of radioactive materials. Instances are: a logarithmic function can be sued to relate the weight of an animal and its lowest galloping speed. Sensation of sound in human ear is logarithmic to its loudness. Scales to measure sound (decibel) is therefore, logarithmic. So is the scale used to measure the magnitude of earthquakes, i.e. the Richter scale.
There are many careers that use exponential and logarithmic functions. Examples of such careers include: astronomer, psychologist , archaeologist, forensic scientist, seismologist etc.