Solving Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, such as a^x = b.

Front

What is the base in an exponential expression?

Back

The number that is raised to a power, for example, in 2^3, 2 is the base.

Front

How do you solve the equation 7^-x = 49?

Back

x = -2, because 49 can be rewritten as 7^2.

Front

What is the first step to solve 4^(p+2) = 64?

Back

Rewrite 64 as a power of 4, which is 4^3.

Front

What is the solution for p in the equation 4^(p+2) = 64?

Back

p = 1.

Front

How do you express 2^(3n) = 4 in terms of base 2?

Back

Rewrite 4 as 2^2, so the equation becomes 2^(3n) = 2^2.

Front

What is the solution for n in the equation 2^(3n) = 4?

Back

n = 2/3.

Front

How can you rewrite 36 = 6^x?

Back

Rewrite 36 as 6^2, so the equation becomes 6^2 = 6^x.

Front

What is the solution for x in the equation 36 = 6^x?

Back

x = 2.

Front

How do you solve the equation 9^(8-x) = 27^(x-3)?

Back

Rewrite both sides with base 3: 9 = 3^2 and 27 = 3^3.