8-4 Properties of Logarithms Use the change of base formula to rewrite and evaluate logs Use properties of logs to evaluate or rewrite log expressions Use properties of logarithms to expand or condense logarithmic expressions Use logarithmic functions to model and solve real-life problems.

Properties of Logarithms Product Property: log a (uv) = log a u + log a v Quotient Property: log a (u/v) = log a u - log a v Power Property: log a u n = n log a u

Using Properties of Logs to find the exact value of the expression Example log 5 3  5 ln e 6 – ln e 2 Rewrite-- log 5 (5) 1/3 Bring exponent out front. 1/3 log 5 (5) = 1/3 Bring exponents out front. 6ln e – 2ln e So-- 6 – 2 = 4 OR we could have rewritten this as division— Ln e 6 = lne 4 = 4lne = 4 e 2

Using Properties of Logarithms to expand the expression as a sum, difference and/or constant ln 2/27 = ln 2 - ln 27 log 3 10z = log log 3 z ln 6  x log 4x 2 y = log 4 + log x 2 + log y = log 4 + 2log x + log y = ln 6 – ln (x 2 + 1) 1/2 = ln 6 – 1/2ln (x 2 + 1)

Write the expression as a single logarithm (Go Backwards) ln y + ln t = ln yt log 8 – log t= log 8/t -4ln 2xt= ln (2xt) -4 2 ln ln (x – 4)= ln ln (x – 4) 5 = ln 8 2 (x – 4) 5 1/3[log x + log (x + 1)]=[log x(x + 1)] 1/3 2[3ln x – ln (x + 1) – ln(x – 1)]=[3ln x – ln (x + 1) – ln(x – 1)] 2 = ln x 3 2 (x + 1)(x – 1) Foil this

Good problems to assign— Page 449 (11-41; 44-49; 58-69;73-87)