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If any time you need to convert multiplications to additions, They can be useful.  For example, if you get a loan at a Bank that has continuous interest (they all do), if you Need to calculate how long it will take to pay it back, you Need to use logarithms.   If you are a scientist studying anything with exponential Growth, like biologists studying populations, physicists Studying nuclear reactions, chemists studying chain Reactions; or a banker calculating how long it will take for Investments to reach certain levels at given interest rates, you need to use logarithms.   If you are a physiologist looking at how the eye reacts to light or the ear to sound, both are so-called "logarithmic devices", i.e., if you double the light or the sound, the reaction of the eye or ear is to signal not a double strength, but rather an increase by a fixed step.  That way you can see light or hear sound in a huge range without having a complex signaling system.   Electrical engineers use logarithms to work on signal decay.  Similarly with communications experts.  Computer scientists looking at how fast programs run with respect to the size of the inputs use logarithms often.  For example, most good sorting programs take time proportional to n*log(n) to sort a list of n items.   There are probably plenty more examples, but these should get you started in thinking about this.

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