Exponential Equation Formula
The exponential equation formula is used to solve the exponential equations. There are two types of exponential equations a) where the bases of the equation on both sides are the same, and b) where the bases on both sides are different. In this section, we will discuss the exponential equations where the bases are the same on both sides. If the bases are same on the both sides, then their power must also be equal to each other. Let us understand the exponential equation formula in detail along with solved examples in the following section.
What is the Exponential Equation Formula?
The exponential equation formula is the equation equating the exponential function, which grows or decays slowly in the beginning and then changes readily with a small change in time. The exponential equation formula for the like bases is given as,
If a^{y}= a^{x}
Then x = y
where,
 a>0 and not equal to 1.
Let us now look at a few solved examples on the exponential equation formula to understand this concept better.
Solved Examples Using Exponential Equation Formula

Example 1: Simplify: 5^{x+}1  5^{x} using exponential equation formula.
Solution:
By using the property exponential equation formula
a^{x+y} = a^{x }a^{y }
5^{x+1} can be written as 5^{x}.5
5^{x+1} – 5^{x} = 5^{x}.5 – 5^{x}
5^{x+1} – 5^{x} = 5^{x}(5 – 1)
5^{x+1} – 5^{x} = 5^{x}(4)
5^{x+1} – 5^{x} = 4 × 5^{x}
Answer: 5^{x+1} – 5^{x} = 4 × 5^{x} 
Example 2: Simplify: 10^{3}  10^{5}^{ }using exponential equation formula.
Solution:
By using the property of exponential equation formula
a^{x+y} = a^{x }a^{y }10^{5 } can be written as 10^{3}.10^{2}
10^{3} – 10^{5 }= 10^{3} – 10^{3}.10^{2}
10^{3} – 10^{5 }= 10^{3}(1  10^{2})
10^{3} – 10^{5 }= 10^{3}(1  100)
10^{3} – 10^{5 }= 10^{3}(99)
10^{3} – 10^{5 }= 99 × 10^{3}
Answer: 10^{3} – 10^{5 }= 99 × 10^{3}