Why do you need to invent a whole new set of mathematical notation, logs, if you could just express the same answer in quicker, less "complex" exponential form?
1 Answer
It is notationally much more convenient in circumstances where logarithms naturally arise. Using exponential form in such circumstances can result in convoluted descriptions.
Explanation:
Suppose you were trying to describe what the integral of
Using the natural logarithm, you can write:
#int \ 1/x \ dx = ln abs(x) + "constant"#
In words: "The indefinite integral of one over
If you expressed this in exponential form, you would write something like:
#e^(int 1/x dx) = Cx#
Does this describe what the integral of
Yes, but only in a convoluted way:
In words: "The indefinite integral of one over
More simply, suppose you were asked to find the solution of:
#e^x = 2#
Without logarithms, you could answer: It is an irrational number, approximately equal to
With logarithms you can say
Often, re-expressing equations that use logarithms in terms of descriptions that do not effectively becomes a convoluted way of speaking about the inverse of exponentiation - i.e. logarithm.
For example, try reformulating the following without logarithms:
#(ln x) (ln y) = c#
