Review: Logarithms Lecture notes Math 1030LogarithmsDefinition of logarithmThe logarithm log10x is the power to which the base 10 must be raised to produce the given number x. Inlog10x, 10 is the base and x is the argument of the logarithm. For example, log10(108) = 8.RulesThere are 4 important rules.(1) log1010x= x(2) 10log10x= x (x > 0)(3) log10xy = log10x + log10y (x > 0, y > 0)(4) log10ax= x log10a (a > 0)Ex.1Let log10(2) = 0.30103. Compute the followings without a calculator.(1) log1016(2) log100.0001(3) log100.5(4) log10106(5) log10200(6) log100.4(7) log10102(8) log1024+ log1010−3(9) 10log10(14)(10) log108, 000(11) log1064Solutions(1) 1.20412(2) −4(3) −0.30103(4) 6(5) 2.30103(6) −0.39794(7) 2(8) −1.79588(9) 14(10) 3.90309(11) 1.806181Review: Logarithms Lecture notes Math 1030How to use Log in this classIf you need to find t in the formulanew value = initial value × 2tTyou will have to solve2tT= Awhere A is a number. In order to do that, first take the log:log102tT= log10Athen use Rule 4:tTlog102 = log10ANow, divide by log102 and you gettT=log10Alog102Finally, multiply by T :t = T ×log10Alog102Ex.2The new value is 16, the initial value is 4, the doubling time is 3 years. Find t. (Solution: 6
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