Logarithms are very useful for lengthy calculation.

There are two types of logs: (1) *log *(2) *ln *(Natural *log*)

(1) The base is 10 in *log*

(2) The base is e in natural *log*

Here, we will discuss the properties of *log*.

**Some important properties with example are given below**:

- If then

**NOTE:**

**Example 1:**

Simplify

**Solution 1:**

**Example 2:**

Simplify

**Solution 2:**

Now, solve the problems bases on *log*. **If any doubt, visit our discussion forum** http://onlinepadho.com/forum/