Prerequisite Skills Curtis, Chris, Camil Properties of Exponents Product rule a n a m =a n+m Ex =5 5 Quotient rule a n /a m =a n-m Ex. 5 5 /5 2 =5 3 Power rule (a n ) m =a nm Ex. (9 3 ) 2 =9 6 Negative exponents a -n =1/a n Ex =1/4 3 Properties of Logarithms Power of a log a logam(n) = m Ex. 9 log9(10) = 10 Base Law log a a m = m log = 10 Product Rule log a n + log a m = log a nm Ex. Log log 2 32 = log Quotient Rule log a n log a m = log a (n/m) Ex. Log log 2 32 = log 2 8 Power Rule nlog a m = log a m n Ex. 3log 2 8 = log 2 512 Converting The exponential function a n =y can be expressed in logarithmic form as log a y=n Ex. 4 3 =64 (exponential) log 4 64=3 (logarithmic) Ex. log =2 (logarithmic) 12 2 =144 (exponential) The Exponential Function y=2 x Ex. The value of a section of land costs $30000 and its value is expected to increase by 15% every 2 years. The logarithmic Function The inverse of y=b x is x=b y Or log b x=y (logarithmic function) y=2 x y=log 2 x Trigonometric Ratios Special Triangles: y=sinx y=cosx y=tanx Radian Measure SYR CXR TYX & SOH CAH TOA C.A.S.T Rule C /2 2 or 0 Examples of finding exact values Transformations of graphs Problem solving Trig Identities