1. 6.4 – Solving Logarithmic Equations and Inequalities Objective: TSW solve logarithmic equations and inequalities.

2. Logarithmic equation – an equation that contains one or more logarithm. REMEMBER… REMEMBER… For x > 0 and b > 0, and b = 1 So…x and b MUST be positive and b can never equal 1 (this is why we have asymptotes in our graphs) Logarithmic form: y = log b x Exponential Form: b y = x.

3. To Solve a Logarithm with Only ONE log…. 1. Rewrite the logarithm 2. Break down each side so bases are equal 3. Solve for the exponent. 4. Check Solution to be sure the number within the log is positive. To Solve a Logarithm with a log on each side… 1. Make sure the log and the base are IDENTICAL. 2. If the logs are identical, then the numbers within in the log are identical so set them equal. 3. Solve for x…YOU MAY HAVE TO FACTOR! 4. Check Solution to be sure x is positive!

4. Examples: Solve Each Equation 1.2.

5. 3.4.

6. 5. 6.

7. Examples…Solve Each Equation 7.

8. Examples…Solve Each Equation 8.

9. Examples…Solve Each Equation 9.

10. Homework! pgs. 504-507 #’s 1-17(odds), 23-29(odds), 49- 57(odds)