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 an exponential equation with the same base?

Back

To solve an exponential equation with the same base, set the exponents equal to each other. For example, if 2^x = 2^5, then x = 5.

Front

What is the first step in solving the equation 8 = 2^(5x + 7)?

Back

The first step is to express 8 as a power of 2. Since 8 = 2^3, rewrite the equation as 2^3 = 2^(5x + 7).

Front

How do you isolate the variable in the equation 7^(-x) = 49?

Back

First, express 49 as a power of 7. Since 49 = 7^2, rewrite the equation as 7^(-x) = 7^2, then set the exponents equal: -x = 2.

Front

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

Back

Convert both sides to the same base: 9 = 3^2 and 27 = 3^3. Rewrite the equation as (3^2)^(8-x) = (3^3)^(x-3) and set the exponents equal.

Front

How do you solve (1/8)^x = 2^3?

Back

Rewrite 1/8 as 2^(-3). The equation becomes 2^(-3x) = 2^3. Set the exponents equal: -3x = 3.

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). This allows you to multiply the exponents.

Front

What is the solution to the equation 3^3 = (3^2)^(2x + 1)?

Back

Set the exponents equal: 3 = 2(2x + 1). Solve for x to find x = 1/4.

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.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean to take the logarithm of both sides of an equation?

Back

Taking the logarithm of both sides allows you to bring down the exponent, making it easier to solve for the variable.