Solving Exponentials w/ Same Bases

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent.

Front

What does it mean to have the same base in exponential equations?

Back

It means that the bases of the exponential terms are identical, allowing for easier comparison of the exponents.

Front

How do you solve an exponential equation with the same base?

Back

Set the exponents equal to each other and solve for the variable.

Front

What is the base of 9 in terms of 3?

Back

9 can be rewritten as 3^2.

Front

What is the base of 27 in terms of 3?

Back

27 can be rewritten as 3^3.

Front

If 3^x = 27, what is x?

Back

x = 3.

Front

What is the first step in solving 9^(8-x) = 27^(x-3)?

Back

Rewrite both sides with the same base.

Front

What is the value of 4^3?

Back

64.

Front

If 2^x = 8, what is x?

Back

x = 3.

Front

What is the relationship between exponents when bases are the same?

Back

If a^m = a^n, then m = n.