Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, such as a^x = b.

Front

How do you solve the equation 8 = 2^(5x + 7)?

Back

Rewrite 8 as 2^3, then set the exponents equal: 3 = 5x + 7.

Front

What is the solution to the equation 8 = 2^(5x + 7)?

Back

x = -⅗.

Front

What is the base of the exponential equation 8 = 2^(5x + 7)?

Back

The base is 2.

Front

How do you solve (-3)^x = (-3)^13?

Back

Since the bases are the same, set the exponents equal: x = 13.

Front

What is the solution to the equation (-3)^x = (-3)^13?

Back

x = 13.

Front

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

Back

Rewrite 4 as 2^2, then set the exponents equal: x = -2.

Front

What is the solution to the equation 2^x = 4^(x + 1)?

Back

x = -2.

Front

When solving exponential equations, what must you first get like?

Back

You must first get like bases.

Front

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

Back

This is the Product of Powers Property.