1. S OLVING E XPONENTIAL AND LOGARITHMIC E QUATIONS Unit 3C Day 5

2. D O N OW Find the value of x. a) log 2 2 5 = x b) log 6 6 11 = x c) log 3 3 4 = x d) log 1.5 1.5 3 = x What is the change of base formula? Also, take a calculator if you do not have your own.

3. E XPONENTIAL E QUATIONS Exponential equation: variable is in the _______________ Equal Powers Property: If two powers with the same base are equal, then their exponents must be equal. Ex.: If 3 x = 3 5, then x = ____.

4. E X. 1: S OLVE BY E QUATING E XPONENTS Solve the equation. a) 4 2 = 4 9 x – 5 b) 5 2 x = 5 –x – 3 c) 3 x = 3 -2 x – 6

5. EX. 2: MAKING LIKE BASES Sometimes, you have to make the base alike before you can equate exponents. a) 2 4 x = 32 x – 1 b) 9 x + 1 = 3 x c) 4 3 x = 8 x + 1

6. R EWRITING AS A LOG When it is not convenient to write each side of an exponential equation using the same base, you can solve the equation by rewriting in logarithmic form and using the change of base formula. Ex.: 4 x = 11

7. E X. 3: S OLVE BY R EWRITING AS IN L OGARITHMIC F ORM Solve the equation. Round to the nearest thousandth. a) 3 x = 5 b) 9 x = 35 c) 10 3 x – 1 = 19 d) 10 2 x + 3 = 115

8. E X. 4: I SOLATING THE E XPONENTIAL Sometimes, you have to isolate the exponential before you can rewrite it. a) 4 x – 5 = 10 b) 10 2 x – 3 + 3 = 20 c) 5 x + 2 + 3 = 25

9. C LOSURE What are the two main approaches to solving exponential equations?