Solving Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, 2^x = 8.

Front

How do you solve the equation 8^(3x+3) = 8^6?

Back

Since the bases are the same, set the exponents equal: 3x + 3 = 6. Solve for x: x = 1.

Front

What is the first step to solve 5^(2x) = 5^(-x)?

Back

Set the exponents equal: 2x = -x. Solve for x: x = 0.

Front

How can you rewrite 8 as a power of 2?

Back

8 can be rewritten as 2^3.

Front

What is the solution to the equation 3^3 = 3^(4x + 2)?

Back

Set the exponents equal: 3 = 4x + 2. Solve for x: x = 1/4.

Front

How do you solve the equation 2^x = 4^(x+1)?

Back

Rewrite 4 as 2^2: 2^x = (2^2)^(x+1) = 2^(2x + 2). Set the exponents equal: x = 2x + 2. Solve for x: x = -2.

Front

What is the base of an exponential function?

Back

The base is the constant that is raised to a power. In the equation y = a^x, 'a' is the base.

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

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

Back

This is known as the Power of a Power Property.

Front

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

Back

This is known as the Quotient of Powers Property.