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EVALUATING LOGARITHMS (using LOG Properties) EXPONENTIAL FORM LOGARITHMIC FORM x = ay logax = y NOTE: Example If no base is given, a base of 10 is understood. Ex. log7 = log107 Calculators are programmed in base 10. Ex. log7 = 0.845098 Calculate, rounding to 1 decimal place where required: a) log100 b) log500 Properties of Logarithms: log a 1 0 ex. log 5 1 log a a x x ex. log 6 6 2 a Example log a x x ex. 8log 8 64 Evaluate each of the following expressions without a calculator: a) log 7 1 b) 5 log5 25 c) 1 log 100 d) log 5 125 e) log 2 (4) f) log 6 36 log 5 25 Example Solve for x in each of the following: a) log x 64 6 b) log 3 x 2 Example Estimate the value of log420 using a “guess & check” method. Example A sample of the radioactive substance X13 with mass P grams, is determined by the given equation where t is the time in years and h is the half-life of the substance. If the half-life of X13 is 4 years and the initial mass of the sample is 1600g, determine how long it will take for the substance to decay to a mass of 100g. t 1 h M(t) P 2 Homework: p.466–467 #3–6, 8–12