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, 2^x = 8.

Front

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

Back

p = 1, because 64 can be expressed as 4^3, so p + 2 = 3.

Front

What is the base in the equation 2^(x+6) = 32?

Back

The base is 2, as it is the number raised to the power of (x+6).

Front

How do you express 32 as a power of 2?

Back

32 can be expressed as 2^5.

Front

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

Back

x = 1/4, because the bases are the same, so set the exponents equal: 3 = 4x + 2.

Front

What is the value of x in the equation 16^(x+5) = 64^(-2)?

Back

x = -8, because 16 can be expressed as 4^2 and 64 as 4^3, leading to the equation 4^(4x + 10) = 4^(-6).

Front

What is the first step in solving an exponential equation?

Back

Identify if both sides of the equation can be expressed with the same base.

Front

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

Back

To isolate the variable means to manipulate the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the logarithm of a number?

Back

The logarithm is the exponent to which a base must be raised to produce that number. For example, log_2(8) = 3 because 2^3 = 8.

Front

How can you check your solution for an exponential equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.