Aim: Log Products & Quotients Course: Alg. 2 & Trig. Aim: How do we use logarithms to find values of products and quotients? Do Now: Evaluate to prove or disprove: log ( ) or log 20.5 = log log 16 log (4.5  16) = log log 16 log (4.5  16) = log log 16 log ( ) = 16 log 4.5

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Properties of Logarithms For any positive numbers M, N, and b, b  1, Each of the following statements is true. log b MN = log b M + log b NProduct Property log b M/N = log b M – log b NQuotient Property log b M k = k log b MPower Property log (3 5) = log 3 + log 5 log (3 / 5) = log 3 – log 5 log 3 5 = 5 log 3 Note: log a (M + N) ≠ log a M + log a N Note: base must be the same

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Model Problems Write each log expression as a single logarithm a.log 3 20 – log 3 4 b.3 log 2 x + log 2 y c.log 8 – 2 log 2 + log 3 Expand each log expression d.log 5 x/y e.log 3r 4 Quotient Property Power and Product Properties Quotient, Power and Product Properties = log 5 x – log 5 y = log log r

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Model Problems Rewrite log 7x 3 Expand log 2 3xy 2 Condense log 2 - 2log x Express in terms of log m and log n log log x log log 2 x + 2log 2 y

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Model Problems Given ln 2  0.693, ln 3  1.099, and ln 7  1.946, use the properties of logs to approximate a) ln 6 b) ln 7/27 ln 6 = ln (2 3) = ln 2 + ln 3   = ln 7 – ln 27 = ln 7 – 3 ln 3  – 3(1.099)  ln 7/27

Aim: Log Products & Quotients Course: Alg. 2 & Trig. Model Problems Use properties of logarithms to rewrite as the sum and/or difference of logs = ln(3x – 5) 1/2 – ln 7 = 1/2 ln(3x – 5) – ln 7 Rewrite the following as a single quantity 1/2 log 10 x – 3 log 10 (x + 1) = log 10 x 1/2 – log 10 (x + 1) 3 =