1. Table of Contents Solving Logarithmic Equations A logarithmic equation is an equation with an expression that contains the log of a variable expression. The following examples will show how to solve this type of equation. Example 1: Solve the equation. Exponentiate both sides of the equation, using base 2. In other words, write both side of the equation as exponents of base 2. Method A

2. Table of Contents Solving Logarithmic Equations Original problem Exponentiate Use inverse property to simplify … Evaluate the exponential …

3. Table of Contents Solving Logarithmic Equations Use the definition of a log to express the equation in exponential form. Method B Original problem Evaluate the exponential …

4. Table of Contents Solving Logarithmic Equations Example 2: Solve the following equation. Get the log expression on the left side by itself. Note that ln is a log with base e.

5. Table of Contents Solving Logarithmic Equations Method A Method B

6. Table of Contents Solving Logarithmic Equations Example 3: Solve the following equation (nearest hundredth). Use the Product property to combine the logs. Note that “log” is a log with base 10. Now either exponentiate (Method A) or use the definition of a log (Method B) to get …

7. Table of Contents Solving Logarithmic Equations Use the quadratic formula to solve for x. Written as decimals (nearest hundredth), the solutions are...

8. Table of Contents Solving Logarithmic Equations Go back and look at the original equation and compare with the answers. Note that for the solution x = - 5.36, the expressions (x - 2) and (x + 4) will both be negative. Since the logarithm of a negative number is undefined, we must throw this extraneous solution out. The solution to the equation is

9. Table of Contents Solving Logarithmic Equations Example 4: Solve the following equation. Use the Quotient property to combine the logs on the left hand side of the equation. Equating the two expressions yields...

10. Table of Contents Solving Logarithmic Equations Solve for x.

11. Table of Contents Solving Logarithmic Equations