Exponential Equation Formula

An exponential equation is a special type of equation in which each side can be expressed in terms of the same base and can be solved using the property of exponents. It is used to express a graph in many things like radioactive decay, compound interest, population growth etc.

The exponential equation will be of the form

\[\large y=ab^{x}\]

Here,
x and y are the variables
a and b are constants.

Solved Example

Question 1: Solve for x: 5 3x – 8 = 252x

Solution

Given,
53x – 8 = 252x

25 can be expressed as a power of 5:
53x – 8 = 52(2x) = 54x
Here, bases are the same. Thus, by equating the exponents,
3x – 8 = 4x
⇒ 4x – 3x = -8
⇒ x = -8

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