1. Using the Properties of Logs

2. You already learned how to solve simple log equations. Now we are going a step or two farther. These equations are solved by isolating the logarithm (sound familiar? ) and then writing an equivalent exponential equation. Remember: Always check your answers! Solve each of the following logarithmic equations. 1. 1.Isolate the log. (Done.) 2. Change to exponential form. 3. Solve. 2. 4. Check. 1.Isolate the log. (Done.) 2. Change to exponential form. 3. Solve. 4. Check. -5

3. 3. 1.Isolate the log. (Done.) 2. Change to exponential form. 3. Solve. 4. Check. + 2 ____________ __ 3 3 ____ __ 4 4

4. 4. 1.Combine to a single log. 2. Change to exponential form. 3. Solve. 4. Check. When two or more logarithms are in the equation, it is necessary to first combine them to a single log using the properties of logs! Product Property Wait! Where did that 10 come from? That’s right. It’s the base of the common log. It slid to the other side.

5. 5. 1.Combine to a single log. 2. Change to exponential form. 3. Solve. 4. Check. Quotient Property Multiply both sides by x+1

6. 6. Algebraically determine the intersection point of the two logarithmic functions shown below. Remember how to solve a system of equations? Are you done?

7. 7. Now we can find the inverses for more complicated logarithmic functions. Given the function Find You have 2 minutes!

8. 8. 1.Combine each side to a single log. 2. Common Bases! No logs needed. 3. Solve. 4. Check. Sometimes, there it is not necessary to write an equivalent exponential expression in order to solve for x. (Just like when we solve exponential equations using common bases, we can solve log equations with a single log on each side of the equation. Product Property

9. 9. 1.Combine each side to a single log. 2. Common Bases! No logs needed. 3. Solve. 4. Check. Quotient Property