1. 7.5 E XPONENTIAL AND L OGARITHMIC E QUATIONS

2. E XPONENTIAL E QUATIONS An exponential equation is an equation containing one or more expressions that have a variable as an exponent. 2x + 5 = 11How do you solve this? So, apply that to this: 5 x-2 =200

3. T O SOLVE EXPONENTIAL EQUATIONS : Try writing them so they have the same base: 8 x =2 x+6 Take the logarithm of both sides.

4. S OLVE AND CHECK : 9 8-x =27 x-3 4 x-1 =5

5. L OGARITHMIC EQUATION A logarithmic equation is an equation with a logarithmic expression that contains a variable. Use the concepts of inverses to play around with this: log 3 (x-5) = 2

6. T O SOLVE L OGARITHMIC EQUATIONS You can solve logarithmic equations by using the properties of logs: If log b x = log b y, then x = y

7. W HAT ABOUT ? log 45x – log 3 = 1 log x + log (x + 9 ) = 1 (*)

8. S OLVE log 4 x 2 = 7 log 6 (2x – 1) = -1

9. S OLVE : log 4 100 – log 4 ( x+ 1) = 1 log 5 x 4 = 8

10. S OLVE : 4 2x =32 1/2 2.4 3x+1 =9 log x –log 10 = 14

11. M ORE : log x + log 5 = 2 log x 2 + log 25 = 2