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 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 3^(2x) = 3^4, then 2x = 4, leading to x = 2.

Front

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

Back

The first step is to recognize that since the bases are the same, you can set the exponents equal: 3 = 4x + 2.

Front

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

Back

The solution is x = ¼.

Front

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

Back

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

Front

What is the solution to the equation 5^(a + 2) = 1/125?

Back

The solution is a = -5.

Front

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

Back

First, express 512 as a power of 2: 512 = 2^9. Then set the exponents equal: x + 1 = 9, leading to x = 8.

Front

What is the value of x in the equation 2^(x + 1) = 512?

Back

The value of x is 8.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the base in the exponential equation 5^(x) = 25?

Back

The base is 5.