Solving Exponential Equations with Common Bases

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, 2^x = 8.

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.

Front

What is the first step in solving the equation 3^(2x) = 27^(x - 4)?

Back

Rewrite 27 as 3^3, so the equation becomes 3^(2x) = 3^(3(x - 4)).

Front

If 3^(2x) = 3^(3(x - 4)), what can you conclude about the exponents?

Back

You can conclude that 2x = 3(x - 4).

Front

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

Back

The solution is x = 12.

Front

How can you express 49 as a power of 7?

Back

49 can be expressed as 7^2.

Front

What is the solution to the equation 7^(-x) = 49?

Back

The solution is x = -2.

Front

What does it mean to solve for x in the equation (-3)^x = (-3)^13?

Back

It means to find the value of x that makes both sides of the equation equal, which is x = 13.

Front

What is the property of exponents that allows you to equate the exponents when the bases are the same?

Back

The property states that if a^m = a^n, then m = n, provided a is not zero.

Front

How do you solve the equation 3^3 = (3^2)^(2x + 1)?

Back

Rewrite the right side as 3^(2(2x + 1)) and set the exponents equal: 3 = 2(2x + 1).