Why do we use logs in a time series model?

The point of using logs is it often helps us create a straight line.  Ln is a natural log ie what must you raise “e” to the power by.  Eg ln of 2.718 is 1 and the ln of 7.389 is 2 and 20.085 is 3.  Note how the raw numbers are rising at an ever increasing rates (2.7, 7.3, 20.1) whereas if we plot a line using the ln values (1,2,3) we get a straight line.

The final step is once we have this straight line using ln values we can make an estimate for Y, but then we need to convert back into raw numbers.  This is why the last step is always e^.  Eg if we calculate Y (using ln) as being 1.54 then this means e^1.54 = raw number giving us 4.66