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 the equation 2^(3n) = 4?

Back

Convert 4 to a power of 2: 2^(3n) = 2^2, so 3n = 2, giving n = 2/3.

Front

What is the first step to solve 5^(-3x - 1) = 25?

Back

Rewrite 25 as a power of 5: 25 = 5^2, so -3x - 1 = 2.

Front

What is the solution for x in the equation 5^(-3x - 1) = 25?

Back

x = -1.

Front

How do you solve the equation 4^(p + 2) = 64?

Back

Rewrite 64 as a power of 4: 64 = 4^3, so p + 2 = 3, giving p = 1.

Front

What is the value of p in the equation 4^(p + 2) = 64?

Back

p = 1.

Front

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

Back

Rewrite 8 as a power of 2: 8 = 2^3, so 3 = 5x + 7.

Front

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

Back

x = -⅖.

Front

What is the base of an exponential function?

Back

The constant factor that is raised to a power, such as in a^x.

Front

What is the exponent in an exponential equation?

Back

The variable or number that indicates how many times the base is multiplied by itself.