Section+3.4

Let b, R, S be elements of the set of all positive real numbers, b ≠ 1 and c is an element of the set of all real numbers.   1. log (RS) = log R + log S   2.  log (R/S) = log R – log S    3. log R = clog R  → expanding  condensing ←  Ex.  Expand: log(8xy^4) <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> log8 + logx + 4logy <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Ex. <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> Expand: ln (√x² + 5) <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> ln (x² + 5)^½ - lnx <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> ½ln (x+5) - lnx <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Ex. <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Condense: lnx^5 -2ln(xy) <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> ln(x^5)**/**[(xy)^2] <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Let a, b, x ˃ 0, a,b ≠ 1: <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> Log x = (log x)**/**(log b) <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Ex. <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> Simplify log 7 <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> 4^x = 7 <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> log4x = log7 <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> (xlog4)/(log4) = (log7)/(log4) <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">  x = 1.404 <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Homework: pg. 317 #3-36 mult. Of 3 <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">3.4 Properties of Logarithms **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';">Change of Base Formula **