2. Exponentials without Same Base and Change Base Rule

3. Objectives I can solve an exponential equation that does not have the same base I can use the Change Base Rule to evaluate log expressions

4. Common Logarithms Your calculator has a button in the 7 th row called LOG. This button will calculate the base 10 common logarithm of a number. Example: log 125 = 2.097 ROUND to 3 decimal places

5. Example log 135 = 2.130

6. Using Logarithms to Solve Exponents So far we have solved exponents using the principle of getting the same base, then setting the exponents equal. There are many times that we cannot get the same base, so we need to solve a different method.

7. Old Problems vs New Solve for x 2 (x+1) = 8 2 (x+1) = 2 3 x+1 = 3 x =2 Solve for x 8 (2x-5) = 5 (x+1) If this problem we cannot get the same base To work this new type problem, we will use logarithms

8. Rule for Logarithms Logarithms can be applied to equations. In any equation, if I do something to one side, I must do the same thing to the other side to keep equality. In these problems, we will take the Common Log of both sides of each equation, then use the Power Property

9. Log Power Property

10. Example

11. Using the Property We will use this property when solving exponential equations that do not have the same base

12. Solve for x 8 (2x-5) = 5 (x+1) log 8 (2x-5) = log 5 (x+1) (2x-5) log 8 = (x+1) log 5 (2x–5) (.9031) = (x+1) (.6990) 1.81x – 4.52 =.699x +.699 1.11x = 5.22 x = 4.70

13. Change of Base Formula

14. Find: log 8 77

15. Find: log 16 64

16. Homework WS 12-5