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

How do you solve exponential equations with the same base?

Back

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

Front

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

Back

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

Front

Solve for x: 9^(8-x) = 27^(x-3)

Back

x = 5.

Front

What is the relationship between 5^(-3x - 1) and 25?

Back

25 can be rewritten as 5^2, allowing for comparison of exponents.

Front

Solve for x: 5^(-3x - 1) = 25

Back

x = -1.

Front

How can you express 4^(x+1) in terms of 2?

Back

4 can be rewritten as 2^2, so 4^(x+1) = (2^2)^(x+1) = 2^(2x + 2).

Front

Solve for x: 2^x = 4^(x+1)

Back

x = -2.

Front

What does it mean if two exponential expressions are equal?

Back

Their bases must be the same or their exponents must be equal.

Front

Solve for x: 3^3 = 3^(4x + 2)

Back

x = 1/4.