Just curious, since we're discussing them this week in my class. Why do we need logarithms? Aren't they just a concoction to express exponents?
Yeah, me, too. I still own about five of them.LOL Why do we need calculators? Aren't they just a crutch to do calculations?
Calculators and computers were prohibited in my schooling and early in my professional career. I can still use a slide rule.
Try differentiating ##f(x) = x^x##
Well, then you have probably covered exponential functions such as y = ex, y = 10x, and the like. Log functions, in an appropriate base, are the inverses of the exponential functions. For example,Don't know what you mean. Haven't covered that yet.
Or, "Same reason we have subtraction and division when we already have addition and multiplication."?Once you decide that exponents are needed and inverse functions are needed, you pretty much already have logarithms. Calling them log is just giving a name to something that is already there, namely, the inverse of an exponential function.