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Exponential and Logarithmic Equations Lesson 5.6 Solving Exponential Equations Graphically 0.110 x 0.5 Given Graphical Solution Graph each side of the equation Use calculator to find intersection y = 0.1 (10x) y = 0.5 Solving Exponential Equations Symbolically Given 0.05 1.15 5 x Isolate the coefficient 1.15 100 with the exponent x Take log of both log 1.15 log100 2 sides x log 1.15 2 Use logarithm properties x Use division 2 x log 1.15 Try It Out Given 3(2 x – 2) = 99 Part of class solve graphically Part of class solve symbolically Logarithmic Equation Consider ln 4x = 1.5 Symbolic solution Raise to the power of the base Use property of logarithms Use Division e1.5 x 4 e ln 4 x e1.5 4x e1.5 Logarithmic Equation Graphical solution of ln 4x = 1.5 As before graph both sides of the equation y = ln 4x y = 1.5 Use calculator to find intersection Try It Out Given log x 2 3 2 log x 1 Will they ever meet again? Part of class solve graphically Part of class solve symbolically 10 102log x1 log x2 3 Now what? Applications Gambling revenues (in billions $) from 1991 to 0.131x 1995 can be modeled by f ( x) 26.6e x is the year, x = 0 is 1991 When did revenues reach $45 billion? Assignment Lesson 5.6 Page 456 Exercises 1 – 57 EOO 73 – 93 EOO