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 exponent.

Front

How do you solve the equation 16^(x+5) = 4^(-6)?

Back

Convert both sides to the same base: 16 = 4^2, so 16^(x+5) = (4^2)^(x+5) = 4^(2(x+5)). Set the exponents equal: 2(x+5) = -6, solve for x to get x = -8.

Front

What is the first step in solving 3^(2x) = 27^(x - 4)?

Back

Rewrite 27 as 3^3: 3^(2x) = (3^3)^(x - 4). Then set the exponents equal: 2x = 3(x - 4).

Front

What is the solution to the equation 4^(p+2) = 64?

Back

Rewrite 64 as 4^3: 4^(p+2) = 4^3. Set the exponents equal: p + 2 = 3, so p = 1.

Front

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

Back

Rewrite 25 as 5^2: 5^(-3x - 1) = 5^2. Set the exponents equal: -3x - 1 = 2, solve for x to get x = -1.

Front

What is the property of exponents used in the equation 3^3 = (3^2)^(2x + 1)?

Back

The property used is (a^m)^n = a^(m*n). Here, set the exponents equal: 3 = 2(2x + 1).

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant that is raised to a power. In the function f(x) = a^x, 'a' is the base.

Front

What does it mean to isolate the variable in an exponential equation?

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the solution to the equation 3^(2x) = 27^(x - 4)?

Back

The solution is x = 12.

Front

How do you express 64 as a power of 4?

Back

64 can be expressed as 4^3 because 4^3 = 64.