Solving 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 exponential equations with the same base?

Back

Set the exponents equal to each other and solve for the variable.

Front

What is the base of an exponential function?

Back

The constant factor that is raised to a power, e.g., in 2^x, the base is 2.

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 5^(2x) = 5^(-x)?

Back

x = 0.

Front

How do you express 1/125 as a power of 5?

Back

1/125 can be expressed as 5^(-3).

Front

What is the solution to the equation 5^(a + 2) = 1/125?

Back

a = -5.

Front

How do you solve the equation 3^3 = 3^(4x + 2)?

Back

Set the exponents equal: 3 = 4x + 2, then solve for x.

Front

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

Back

x = 1/4.

Front

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

Back

Rewrite 4 as 2^2, then set the exponents equal.