Ch. 3 – Exponential and Logarithmic Functions 3.3 – Properties of Logarithms

Properties of Logarithms 3 basic properties: loga x + loga y = loga (xy) loga x – loga y = loga (x/y) loga xy = y loga x Ex: Condense each logarithmic expression. Condense doesn’t mean evaluate! log 8 + log 12 – log 3 log (8•12/3) = log (32) 2 ln(x + 2) – ln x

Change of Base Ex: Evaluate log4 29. Set it equal to x, then scoop the loop! 4x = 29 log 4x = log 29 x log 4 = log 29 x = (log 29)/(log 4) x = 2.429 To evaluate non-base-10 logs on your calculator, use the change of base formula:

Expand completely: log4 5x3y 3 log4 5x + log4 y log4 5y + 3 log4 x log4 5 + log4 x3 + log4 y log4 5 + 3 log4 x + log4 y log4 5 • 3 log4 x • log4 y

Expand completely: 2 ln(4x + 1) + 2 ln x ½ ln(4x + 1) – 2 ln x

Condense completely:

Evaluate: log6 .01 -2.570 -1.285 -.333 2.570 1.285