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11/11/2014 5.3: Exponential and Logarithmic Equations Solving Exponential Equations Change of Base Solving Logarithmic Equations Solving Exponential Equations = ( ) Using logarithmic form: Rewrite the equation with the term containing the exponent by itself on one side. Divide both sides by the coefficient of the term containing the exponent. Change the new equation to logarithmic form. Solve for the variable. The term containing the exponent is already by itself. Divide both sides by 150 (the coefficient) 20 = 10 4 = 20 = 20 ≈ 0.32526 4 Solving Exponential Equations = Using logarithmic properties: Rewrite the equation with a base raised to a power on one side. Take the logarithm, base e (ln) or 10, of both sides of the equation. Use a logarithmic property to remove the variable from the exponent. Solve for the variable. The equation already has a base raised to a power. Take the log base 10 4096 = 8!" Power Property of Logarithms 4096 = 2#8 4096 == 28 1 11/11/2014 Change of Base Used to rewrite logarithms so that the base is 10 or e For base 10 and base e $ # = %&' " %&' $ $ # = %( " %( $ Solving Logarithmic Equations Graphically Graph the left and right sides of the equation separately Find the point of intersection Algebraically Convert to exponential form Solve 2