Solving Exponential Equations

Front

What is an exponential equation?

Back

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

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. For example, if 3^x = 3^4, then x = 4.

Front

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

Back

The first step is to recognize that both sides of the equation have the same base (3), allowing you to set the exponents equal: 3 = 4x + 2.

Front

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

Back

x = 1/4.

Front

What does it mean to have a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, 2^-3 = 1/(2^3) = 1/8.

Front

How do you solve the equation 2^-m = 2^(3m - 3)?

Back

Set the exponents equal: -m = 3m - 3, then solve for m.

Front

Solve for m: 2^-m = 2^(3m - 3)

Back

m = 3/4.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This property states that when multiplying two exponential expressions with the same base, you can add the exponents.

Front

Solve for n: 2^-2n = 2^6

Back

n = -3.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.