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 exponential equations with the same base?

Back

To solve exponential equations with the same base, set the exponents equal to each other and solve for the variable. For example, if 3^(3) = 3^(4x + 2), then set 3 = 4x + 2.

Front

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

Back

The first step is to set the exponents equal to each other: 3 = 4x + 2.

Front

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

Back

The solution is x = 1/4.

Front

How do you solve an exponential equation with a negative base?

Back

When solving an exponential equation with a negative base, ensure that both sides of the equation have the same base and that the exponents are equal. For example, in (-3)^x = (-3)^13, set x = 13.

Front

What is the solution to the equation (-3)^x = (-3)^13?

Back

The solution is x = 13.

Front

How can you express 9^(8-x) in terms of base 3?

Back

9 can be expressed as 3^2, so 9^(8-x) = (3^2)^(8-x) = 3^(2(8-x)) = 3^(16 - 2x).

Front

What is the solution to the equation 9^(8-x) = 27^(x-3)?

Back

The solution is x = 5.

Front

How do you convert the equation 4^(p+2) = 64 into a base of 4?

Back

64 can be expressed as 4^3, so the equation becomes 4^(p+2) = 4^3.

Front

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

Back

The solution is p = 1.