I'm currently working on an iOS & Android application for GCE O Level students. I have to classify everything neatly such that Maths never appears to be a messy subject to study and so
should I classify logarithm into arithmetic or algebra?
Here is the definition of arithmetic by Oxford dictionary:
the branch of mathematics dealing with the properties and manipulation of numbers.
and the definition of algebra:
the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations
According to this, there would be an inconsistency.
The usage of logarithm is considered arithmetic since it is manipulating number.
$Log_{10} 100 = 2$
And the laws of logarithms would be considered algebra.
$Log_b (MN) = Log_b (M) + Log_b (N)$
This really frustrates me because I will have to classify the usage of logarithm and the laws of logarithm into different branches of mathematics but they are both under the same group.
What should I do?