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 4^(p+2) = 64?

Back

Rewrite 64 as 4^3. Then, set the exponents equal: p + 2 = 3. Solve for p: p = 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

How do you rewrite 8 as a power of 2?

Back

8 can be rewritten as 2^3, since 2 multiplied by itself three times equals 8.

Front

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

Back

Rewrite 27 as 3^3. Then, set the exponents equal: 2x = 3(x - 4). Solve for x: x = 12.

Front

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

Back

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

Front

What is the first step in solving an exponential equation?

Back

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

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 logarithm of a number?

Back

The logarithm of a number 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 do you solve for p in the equation 4^(p+2) = 64?

Back

Convert 64 to base 4: 64 = 4^3. Set p + 2 = 3, then solve for p: p = 1.