Exponential Equations
Grade 10 · Algebra
1. Definition
An exponential equation is an equation in which the unknown variable appears in the exponent.
Examples of exponential equations:
- $2^x = 16$
- $3^{2x-1} = 27$
- $5^{x^2 - 3x} = 125$
⚡ Fundamental Principle
Solving exponential equations often reduces to the form:
$$a^x = a^b \quad \text{where } a > 0,\; a \neq 1$$
Key Rule: Powers with the same base $a > 0$, $a \neq 1$ are equal if and only if their exponents are equal:
$$a^{x_1} = a^{x_2} \;\Longleftrightarrow\; x_1 = x_2$$
📊 Interactive: Explore Exponential Functions
Drag the slider to change the base $a$ and observe how $y = a^x$ behaves. Notice that $a^x > 0$ always!
Interactive visualization — available in the full lesson