Logarithms and Properties
1.0 Introduction
1.0 Introduction
Logarithm are used for complicated numerical calculations.
It converts the product and division process to addition and substraction respectively.
We study logarithm for the real number system only.
A number $x$ is called the logarithm of a number $N$ to the base $a$ if,
$$\begin{equation} \begin{aligned} a > 0 \\ a \ne 1 \\ N > 0 \\\end{aligned} \end{equation} $$
then,$${\log _a}N = x$$ or $${a^x} = N$$
The above condition, $a>0$, $a \ne 1$ and $N>0$ is necessary for the ${\log _a}N = x$ to be defined.
If these conditions are not satisfied, then the logarithm ${\log _a}N = x$ is not defined.
Let us assume different cases when,
- $a=1$
- $a=0$
- $N<0$ or $N$ is negative
