Exponential Equations

Front

Define an exponential equation.

Back

An exponential equation is an equation in which a variable appears in the exponent, typically in the form a^x = b, where a and b are constants.

Front

What is the base in an exponential equation?

Back

The base is the constant 'a' in the exponential expression a^x.

Front

How do you solve an exponential equation with the same base?

Back

If a^x = a^y, then x = y.

Front

Solve for x: (-3)^x = (-3)^13

Back

x = 13.

Front

Solve for x: 3^3 = 3^(4x + 2)

Back

x = 1/4.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This is known as the Product of Powers Property.

Front

Solve for x: 5^(-3x - 1) = 25

Back

x = -1.

Front

What is the Quotient of Powers Property?

Back

The Quotient of Powers Property states that a^m / a^n = a^(m-n).

Front

Solve for x: 9^(x+8) = 81

Back

x = -6.

Front

What is the Power of a Power Property?

Back

The Power of a Power Property states that (a^m)^n = a^(m*n).