About Exponential Equations
Exponents are used in exponential equations, as the name implies. The exponent of a number (base) indicates how many times the number (base) has been multiplied. But what happens when a number's power is a variable? An exponential equation is one in which power is a variable and is a part of an equation. To answer exponential equations, we may need to apply the relationship between exponents and logarithms.
What do you mean by Exponential Equations?
An exponential equation in which the exponent (or a portion of the exponent) is a variable. Examples of exponential equations include 3x = 81, 5x - 3 = 625, 62y - 7 = 121, and so on. When tackling problems involving algebra, compound interest, exponential growth, and exponential decay, we may encounter the application of exponential equations.
Exponential Equations Types:
There are three types of exponential equations, as follows:
Equations with the same bases on both sides. (Example: 4x = 42)
Equations with different bases can be made the same. (Example: 4x = 16 which is written as 4x = 42)
Equations that can't be made the same since they have distinct bases. (Example: 4x = 15)
Formulas for Exponential Equations
Bases on both sides of the exponential equation may or may not be the same when solving it. Example: 4x = 42, 4x = 15
Equality for Exponential Equations Property:
When solving an exponential equation with the same bases, this characteristic comes in handy. When bases on both sides of the exponential equation are equal, the exponents must likewise be equal, according to this rule. ax = ay <=> x = y.
Logarithmic Form of Exponential Equations
We all know that exponents are logarithms and vice versa. As a result, a logarithmic function can be created from an exponential equation. This aids in the solution of an exponential equation with multiple bases. The formula for converting exponential equations to logarithmic equations is given below.
bx = a <=>logba = x
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