10.2 Logarithms and Logarithmic Functions

1. 10.2 Logarithms and Logarithmic Functions Algebra II w/trig

2. A logarithm is another way to write an exponential. A log is the inverse of an exponential. Definition of Log function: The logarithmic function with base b where b>0 and b ≠ 1, is denoted by logb and is defined by: if and only if by = x When converting from log form or vice versa b is your base, y is your exponent and x is what you exponential expression equals.

3. Write each equation in logarithmic form. • 35 = 243 • 25 = 32 • 4-2 = 1/16 • (1/7)2

4. II. Write each equation in exponential form. • log2 16 = 4 • log10 10 = 1 • log5 125 = 3 • log8 4 = 2/3 • log10 0.001= -3

5. III. Evaluating Log -- set the log equal to x -- write in exponential form -- find x -- remember that logs are another way to write exponents A. log8 16 B. log2 64

6. log10 100000 D. log5 m = 4 E. log3 2c = -2

7. If their bases are the same, exponential and logarithmic functions “undo” each other. a. log9 92 = x b. 7log7(x2-1)

8. IV. Property of equality for log functions - If a is a positive # other than 1, then loga x = loga y, if and only if x=y. • Solve each equation and CHECK your solutions. 1. log4(3x-1)= log4(x+3) 2. log2(x2-6) = log2(2x +2)

9. 3. logx+4 27 = 3 (Hint: rewrite as exponential, then solve.) 4. logx 1000 = 3

10. 5. log8 n = 4/3 6. log4 x2= log4(4x-3)