Chapter 4: Logarithms and Exponents 2.0 / 5 MathematicsLogarithms and exponentialsInternational BaccalaureateOther Created by: MillyCreated on: 17-04-13 16:34 Law of exponents a^m * a^n = a^(m+n) a^m / a^n = a^(m-n) (a^m)^n = a^(mn) a^0 = 1 n√ a = a^(1/n) n√ (a^m) = (n√ a)^m = (a^m)^(1/n) = (a^1/n)^(m) = a^(m/n) 1 of 6 Exponential functions An exponential function is a function of the form f(x) = a^x when a is a positive real number (that is, a>0) and a ≠ 1. The domain of the exponential function is the set of all positive real numbers The range of the exponential function is the set of all positive real numbers The graph of the exponential function f(x) = e^(-x) is a graph of exponential decay 2 of 6 Logarithms properties a=b^c then c=logb(a) loga(a) = 1 loga(a) = 0 loga(b) is undefined for any negative base. loga(0) is undefined loga(a^n) = n 3 of 6 Logarithmic functions Generally is f:x → a^x then f^-1:x→loga(x) y=loga(x) is the inverse of y=a^x y=Ln(x) is the inverse of the exponential function y=e^x loga(a^x) = x and a^(loga(x)) = x Ln(e^x) = x and e^(Ln(x)) = x log(10x) = x and (10^log(x)) = x 4 of 6 Laws of logarithms log(x) + log(y) = log(xy) log(x) - log(y) = log(x/y) log(x'^n) = nlog(x) log(1/x) = -log(x) 5 of 6 Change of base formula logb(a) = (logc(a))/(logc(b)) 6 of 6

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