Solving Exponential Equations

Front

Define an exponential equation.

Back

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

Front

What is the base in an exponential expression?

Back

The base is the number that is raised to a power in an exponential expression, e.g., in 5^x, 5 is the base.

Front

How do you solve the equation 5^(2x) = 5^(-x)?

Back

Since the bases are the same, set the exponents equal: 2x = -x. Solving gives x = 0.

Front

What is the property of exponents that allows you to set exponents equal when bases are the same?

Back

If a^m = a^n, then m = n, provided a > 0 and a ≠ 1.

Front

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

Back

Set the exponents equal: 3 = 4x + 2. Solving gives x = 1/4.

Front

What is the relationship between 2^x and 4^(x+1)?

Back

4 can be rewritten as 2^2, so 4^(x+1) = (2^2)^(x+1) = 2^(2x + 2). Thus, 2^x = 2^(2x + 2) leads to x = -2.

Front

How do you rewrite 25 in terms of base 5?

Back

25 can be rewritten as 5^2.

Front

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

Back

Rewrite 25 as 5^2. Set the exponents equal: -3x - 1 = 2. Solving gives x = -1.

Front

What is the solution to the equation 8^(3x + 3) = 8^6?

Back

Set the exponents equal: 3x + 3 = 6. Solving gives x = 1.

Front

What is the first step in solving an exponential equation?

Back

Identify if the bases can be made the same or if logarithms need to be used.