Exponential equations

Exponential equation is a form of equation that has powers of the unknown that is not equal to 1, but it is not necessarily a quadratic equation.

Laws of exponential equations

There are two (2) laws of exponential equations and they are

Law1

In an exponential equation, if the bases are equal, then the powers are equated

Example

If x³ = x^y , then 3 = y (y = 3) since the bases are equal.

Law2

In an exponential equation, if the powers are equal, then the bases are equated

Example1

x³ = 2³ , then x=2 (since the powers are equal)

Example 2

Solve the equation r³ = 64

Solution

Given that r³ = 64

Remember that 64 = 4 * 4 * 4 = 4³

^{So, in place of} 64^{, we write} 4^{3 in the equation as follows}

r³ = 64 becomes

r³ = 4³

r = 4 (since the powers are equal)