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 3^3 = 3^(4x + 2)?

Back

Since the bases are the same, set the exponents equal: 3 = 4x + 2.

Front

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

Back

x = 1/4.

Front

How can you express 8 as a power of 2?

Back

8 can be expressed as 2^3.

Front

What is the solution to the equation 8 = 2^(5x + 7)?

Back

x = -4/5.

Front

What is the relationship between logarithms and exponential equations?

Back

Logarithms can be used to solve exponential equations by converting them into linear equations.

Front

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

Back

1/125 can be rewritten as 5^(-3).

Front

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

Back

a = -5.

Front

What is the value of p in the equation 4^(p + 2) = 64?

Back

p = 1.