Indices and Logarithms

Laws of Rational Exponents of Real Numbers

Let us suppose we are given 3 numbers: 2, 3 and 9.

Now, we know that 3^{2} = 9

Also, $\sqrt{9}=3$

The above two expressions are formed by combining 2 and 3, and 2 and 9 respectively to get the third number.

Is there an expression wherein we can combine 3 and 9 to get 2?

3 and 9 can be combined to get 2 as:

Here, ‘log’ is the abbreviated form of a concept called ‘Logarithms’.

The expression can be read as ‘logarithm of 9 to the base 3 is equal to 2’.

In general, if *a* is any positive real number (except 1), *n* is any rational number such that , then *n* is called the logarithm of* b* to the base *a*, and is written as.

Thus, if and only if .

is called the exponential form and is called the logarithmic form.

**The following are the properties of logarithms.**

1. Since *a* is any positive real number (except 1), *a*^{n} is alwa…

To view the complete topic, please