In Exercises 93–102, solve each equation. 5^(x^2−12)=25^2x

Key Concepts

Exponential Equations

Exponential equations involve variables in the exponent and can often be solved by rewriting them in a common base. In this case, both sides of the equation can be expressed as powers of 5, which simplifies the process of finding the variable's value.

Properties of Exponents

Understanding the properties of exponents is crucial for manipulating exponential expressions. Key properties include the product of powers, power of a power, and the power of a product, which allow us to combine and simplify terms effectively when solving equations.

Quadratic Equations

The equation may lead to a quadratic form after simplification. Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, and they can be solved using factoring, completing the square, or the quadratic formula, depending on the context of the problem.