pre calculus

Properties of Logarithms The following properties serve to expand or condense a logarithm or logarithmic expression so it can be worked with. Properties of logarithms Example log mn = log m +logan log, 3x = log, 3 +log4 x m = logam -logan 1082 5 1 =log2 (x+1) -10g2 5 10gan log m" = nlog. m log , ( 2x +1 ) = 31083 (2x+1) Properties of Natural Logarithms Example In mn = In m + Inn In (x +1) (x-5) = In(x+1) +In(x-5) In - = Inm -Inn In ~ = Inx -In 2 n 2 In m" = nlnm In 73 = 3 In 7 These properties are used backwards and forwards in order to expand or condense a logarithmic expression. Therefore, these skills are needed in order to solve any equation involving logarithms. Logarithms will also be dealt with in Calculus. If a student has a firm grasp on these three simple properties, it will help greatly in Calculus. Expanding Logarithmic Expressions Write each of the following as the sum or difference of logarithms. In other words, expand each logarithmic expression. 3x3 1 2 A) 10g2 25 B) log, 53xy2 C) log 4(x + 1) (x -2)2 6x2 D) 1085 1 1yz 167