How To Find The Base Of a Logarithm

Finding the base of a log is very simple.Before coming to the topic it is very important to

know the parts of a logarithm.The logarithm has three parts. Which are base, power and

exponent. If power and exponent are given in the problem, we can find the base.

For example: Logₓ 36=2

Here base is x, 36 is power, and 2 is exponent.

To find the base follow these four steps.

1.Write the given problem into exponential form.

First of all convert the logarithmic form into exponential form.

For Example:

Logₓ  16 = 2

x²=16

2. Convert the power into exponential form.

In our example the power is 16. So it will be equal to  4² or 2⁴.

x²=4²

3. Multiply the exponent of unknown base with its multiplicative

inverse on both sides.

The exponent of x is 2 in the above example. So its multiplicative inverse will be 1⁄2 .

(x²)1⁄2 =(4²)1⁄2

4. Solve the multiplication of the exponents to get the answer.

So exponent 2 and ½  will cancel each other and we will get our answer.

x=4

 So the base of the above logarithmic problem is 4.