# Algebra II w/trig. A logarithm is another way to write an exponential. A log is the inverse of an exponential. Definition of Log function: The logarithmic.

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Algebra II w/trig

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 log b and is defined by: if and only if b y = 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.

I. Write each equation in logarithmic form. A. 3 5 = 243 B. 2 5 = 32 C. 4 -2 = 1 / 16 D. ( 1 / 7 ) 2

II. Write each equation in exponential form. A. log 2 16 = 4 B. log 10 10 = 1 C. log 5 125 = 3 D. log 8 4 = 2/3 E. log 10 0.001= -3

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. log 8 16B. log 2 64

C. log 10 100000 D. log 5 m = 4 E. log 3 2c = -2

F. If their bases are the same, exponential and logarithmic functions “undo” each other. a. log 9 9 2 = x b. 7 log 7 (x 2 -1)

IV. Property of equality for log functions - If a is a positive # other than 1, then log a x = log a y, if and only if x=y. A. Solve each equation and CHECK your solutions. 1. log 4 (3x-1)= log 4 (x+3) 2. log 2 (x 2 -6) = log 2 (2x +2)

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

5. log 8 n = 4 / 3 6. log 4 x 2 = log 4 (4x-3)

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