1. 7-5 PROPERTIES OF LOGARITHMS Rolling them out and Wrapping them up

2. Definitions  1. Product Property   2. Quotient Property   3. Power Property   The above will be on the quiz!

3. Product Property  b, m, & n must be positive numbers and b ≠ 1  log b mn = log b m + log b n  Examples:  log 4 21 = log 4 (3 · 7) = log 4 3 + log 4 7  log 3 27 = log 3 (3 * 9) = log 3 3 + log 3 9 = 1 + 2 = 3  log 3 4x = log 3 4 + log 3 x

4. Quotient Rule  b, m, & n must be positive numbers and b ≠ 1  log b = log b m – log b n  Examples:  log 4 = log 4 3 – log 4 7  log 3 = log 3 2 – log 3 x  Notice the numerator is listed first and the denominator is subtracted from it mnmn 3737 2x2x

5. Power Property  b, m, & n must be positive numbers and b ≠ 1  log b m n = n log b m  Examples:  log 4 49 = log 4 7 2 = 2 log 4 7  log 2 512 = log 2 8 3 = 3 log 2 8 = 3 · 3 = 9

6. Using properties to expand an expression  log 6 = log 6 5x 3 – log 6 y Quotient Property = log 6 5 + log 6 x 3 – log 6 y Product Property = log 6 5 + 3 log 6 x – log 6 y Power Property 5x 3 y Using properties to condense an expression  5 log 4 2 + 7 log 4 x – 4 log 4 y  log 4 2 5 + log 4 x 7 – log 4 y 4 Power Property  log 4 2 5 x 7 – log 4 y 4 Product Property  log 4 = log 4 Quotient Property & Simplify 25x7y425x7y4 32x 7 y 4

7. Change of Base Formula  log 3 8 = ≈ ≈ 1.893 log 8 log 3 0.9031 0.4771