1. INTRODUCTION TO LOGARITHMS 5 5

2. WHAT YOU SHOULD LEARN: I can convert logarithmic expressions to exponential expressions and vice versa. I can evaluate logarithmic functions.

3. 2.4 I can convert logarithmic expressions to exponential expressions and vice versa.

4. WHAT IS A LOGARITHM?  Definition of a Logarithm  If b > 0, b ≠ 1, and x > 0, then  Logarithmic Form Exponential Form log b x = y iffb y = x base exponent base exponent Remember: A logarithm is an exponent!

5. CONVERT EACH LOGARITHMIC EXPRESSION TO AN EQUIVALENT EXPONENTIAL EXPRESSION. ① Log 3 81 = 4 ① Log 2 = -3 ② Log 10 100 = 2 ③ Log 5 = -3 ④ Log 27 3 = 3 4 = 815 -3 = 1/125 2 -3 = 1/827 1/3 = 3 10 2 = 100

6. CONVERT EACH EXPONENTIAL EXPRESSION TO AN EQUIVALENT LOGARITHMIC EXPRESSION. ① 9 2 = 81 ② 5 4 = 625 ③ 12 -2 = ④ 10 2 =100 ⑤ Log 9 81 = 2log 10 100 = 2 Log 5 625 = 4log 5 √5 = 1/2 log 12 1/144 = -2

7. THE COMMON LOGARITHM  A logarithm with base 10 or log 10 is called a common logarithm.  The common logarithm is often written without the base.  y = logxiff10 y = x

8. THE NATURAL LOGARITHM RECALL: E ≈ 2.71828…  A logarithm with base e or log e is called a natural logarithm.  The natural logarithm is often written without the base.  y = lnxiffe y = x

9. CONVERT EACH EXPONENTIAL EXPRESSION TO AN EQUIVALENT LOGARITHMIC EXPRESSION OR VICE VERSA. ① Log x = 2 ② Ln 20.0855… ≈ 3 ③ e 4 ≈ x ④ 10 6 = 1,000,000 10 2 = x e 3 ≈ 20.0855… Ln x = 4 Log 1,000,000 = 6

10. EVALUATE THE FOLLOWING: ① log   = x ① log  /   /  = x ① Log x  = 3 ② log  x = 0 ① log  x = -2 ① Log x  /   /  19 x = 361 x = 2 3 0 = x x = 1 (1/7) x = 1/49 x = 2 9 -2 = x x = 1/81 x 3 = 216 x = 6 X -1/4 = 1/2 x = 16

11. 2.5 I can evaluate logarithmic functions in a real world scenario.

12. A solution’s pH is given by the function p(t)   log(t), where t is the hydronium ion concentration, in moles per liter. A sample of coffee has a pH of 5.0. What is the approximate hydronium ion concentration of the sample?

13. The wind speed s (in miles per hour) near the center of a tornado is related to the distance d (in miles) the tornado travels by the equation s = 93logd + 65. a. On March 18, 1925, a tornado whose wind speed was about 280 miles per hour struck the Midwest. How far did the tornado travel?