Solve Exponential Equations (no logs)

Front

Define an exponential equation.

Back

An exponential equation is an equation in which a variable appears in the exponent, typically in the form a^x = b, where a and b are constants.

Front

What is the first step to solve an exponential equation with the same base on both sides?

Back

Set the exponents equal to each other. If a^m = a^n, then m = n.

Front

Solve for x: 5^{-3x - 1} = 25

Back

x = -1

Front

Solve for x: 8^3x+3 = 8⁶

Back

x = 1

Front

Solve for n: 2^-2n = 2⁶

Back

n = -3

Front

Solve for x: 3³ = 3^{4x + 2}

Back

x = ¼

Front

Solve for x: 2^x+6 = 2⁵

Back

x = -1

Front

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

Back

This is known as the Product of Powers Property.

Front

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

Back

This is known as the Power of a Power Property.

Front

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

Back

This is known as the Quotient of Powers Property.