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, in the equation 2^x = 8, x is the variable in the exponent.

Front

How do you solve the equation 5^(a + 2) = 1/125?

Back

To solve for a, rewrite 1/125 as 5^(-3). Thus, a + 2 = -3, leading to a = -5.

Front

What is the property of exponents used in the equation (-3)^x = (-3)^13?

Back

The property states that if the bases are the same, then the exponents must be equal. Therefore, x = 13.

Front

How do you solve the equation 5^(-3x - 1) = 25?

Back

Rewrite 25 as 5^2. Set the exponents equal: -3x - 1 = 2, leading to x = -1.

Front

What does the equation 8^(3x + 3) = 8^6 imply about the exponents?

Back

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

Front

How do you express 64 as a power of 4 in the equation 4^(p + 2) = 64?

Back

Rewrite 64 as 4^3. Set the exponents equal: p + 2 = 3, leading to p = 1.

Front

What is the first step in solving exponential equations?

Back

The first step is often to express both sides of the equation with the same base, if possible.

Front

What is the inverse operation of an exponential function?

Back

The inverse operation is the logarithm. For example, if y = a^x, then x = log_a(y).

Front

What is the base of an exponential function?

Back

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

Front

What is the solution to the equation 5^(x) = 25?

Back

Rewrite 25 as 5^2. Therefore, x = 2.