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

2. D O N OW How would you solve the exponential equation 3 x + 1 = 3 2 x – 5 ? How would you solve the exponential equation 3 x +1 = 4?

3. L OGARITHMIC E QUATIONS Let’s call “the thing we’re taking the log of” the argument. In log b x = y, the argument is ___. Logarithmic equation: variable is in the ________________ Equal Logarithms Property: If two logs with the same base are equal, then their arguments are equal. Ex.: If log 2 x = log 2 7, then x = ______.

4. E X. 1: S OLVE BY E QUATING A RGUMENTS Solve the equation. a) log 7 (4 x – 3) = log 7 ( x + 6) b) log 4 (2 x + 8) = log 4 (6 x – 12) c) log 5 (4 x – 7) = log 5 ( x + 5)

5. R EWRITING IN E XPONENTIAL F ORM If a log equation is not of the form log b a = log b c, then you can solve by rewriting each in exponential form. Ex.: log 4 (5 x – 1) = 3

6. E X. 2: S OLVE BY R EWRITING IN E XPONENTIAL F ORM Solve each equation. a) log 2 (3 x + 1) = 4 b) log 7 (3 x – 2) = 2

7. E X. 3: I SOLATING L OGS Sometimes you have to isolate the logarithm first before you can rewrite in exponential form. a) 5 + log 4 ( x + 3) = 7 b) 4log 3 x = 28 c) 3log 5 (3 x + 1) – 2 = 4

8. CLOSURE Explain how to solve a logarithmic equation when both sides of the equation are logs of like bases. Explain how to solve a logarithmic equation when both sides are not logs.