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 5^(a + 2) = 1/125?

Back

To solve, rewrite 1/125 as 5^(-3). Thus, a + 2 = -3, leading to a = -5.

Front

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

Back

Convert 8 to a power of 2: 8 = 2^3. Then set the exponents equal: 3 = 5x + 7.

Front

How do you solve the equation 2^(x + 1) = 512?

Back

Rewrite 512 as a power of 2: 512 = 2^9. Set the exponents equal: x + 1 = 9, leading to x = 8.

Front

What is the solution to the equation 4^(3b - 3) = 1/16?

Back

Rewrite 1/16 as 4^(-2). Thus, 3b - 3 = -2, leading to b = 1/3.

Front

What is the base of an exponential function?

Back

The base is the constant that is raised to a power. In the function f(x) = a^x, 'a' is the base.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This is known as the Product of Powers Property.

Front

What is the property of exponents that states (a^m)^n = a^(m*n)?

Back

This is known as the Power of a Power Property.

Front

What is the property of exponents that states a^m / a^n = a^(m-n)?

Back

This is known as the Quotient of Powers Property.

Front

How do you express 1/125 as a power of 5?

Back

1/125 can be expressed as 5^(-3).