Unit 3, Lesson 5

exponential equation

equations that contain the form b^cx, sudch as a = b^cx where the exponent includes a variable

What is important to remember when working with logs?

logs are defined only for positive numbers; the log of a negative number is undefined

Solving Double-Sided Log Equations

1. Equate powers (Ex: log5(5x - 1) = log5(x + 7) 2. Use 1-1 Property (Ex: 5x - 1 = x + 7) 3. Simplify & solve 4. Check solutions using original equation to find extraneous solutions

Solving an Exponential Equation - Different Bases

Ex: 15^3x = 285 1. Take the logarithm of each side (Ex: log 15^3x = log 285) 2. Use the Power Property of Logarithms (Ex: 3x log 15 = 285) 3. Divide to isolate x (Ex: x = log 285/3 log 15) 4. Use a calculator (Ex: x = 0.6958) 5. Check using original equation

Solving an Exponential Equation - Common Base

Ex: 16^3x = 8 1. Rewrite the terms with a common base (Ex: (2^4)^3x = 2^3) 2. Use the Power Property of Exponents (Ex: 2^12x = 2^3) 3. If 2 numbers with the same base are equal, their exponents are equal (Ex: 12x = 3) 4. Solve & simplify (Ex: x = 1/4)

Solving a Logarithmic Equation Using Exponents

Ex: log (4x - 3) = 2 1. Write in exponential form (Ex: 4x - 3 = 10^2) 2. Simplify (Ex: 4x = 103) 3. Solve for x (Ex: x = 103/4 = 25.75)

Using Logarithmic Properties to Solve an Equation

Ex: log (x - 3) + log x = 1 1. Use the Product Property of Logarithms (Ex: log ((x - 3)x) = 1) 2. Write in exponential form (Ex: (x - 3)x = 10^1) 3. Simplify to a quadratic equation in standard form (Ex: x^2 - 3x - 10 = 0) 4. Factor the trinomial (Ex: (x - 5)(x + 2) = 0) 5. Solve for x (Ex: x = 5 or x = -2) 6. Check solutions using original equation to find extraneous solutions

logarithmic equation

an equation that includes 1 or more logarithms involving a variable