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.
