3.3 Properties of Logarithms Change of base formula log a x =or

Ex. log 4 30 = log 2 14 = Properties of Logarithms 2. log u/v = log a u – log a v 3. log a u n = n log a u 2. ln u/v = ln u – ln v 3. ln u n = n ln u 1. log a (uv) = log a u + log a v 1. ln(uv) = ln u + ln v

Use the logarithmic properties to expand the following. log 10 5x 3 y= log 5 + log x 3 + log y = log 5 + 3log x + log y ln (3x – 5) 1/2 – ln 7 ln 1 – (ln x + ln y) = 0 - ln x – ln y

Condensing a log function 2 ln (x + 6) + ln x =ln x(x + 6) 2 ln x - ln y + ln z =