OBJECTIVESLearn how to •Use like bases to solve exponential equations•Use logarithms to solve exponential equations•Use the definition of a logarithm to solve logarithmic equations•Use one to one property of logarithms to solve logarithmic equations•Solve applied problems involving exponential and logarithmic equations
Properties used to solve Exponential and Logarithmic Equations •One to one propertiesax= ayif, and only if x=ylogax = logay if, and only if x = y.•Inverse properties: logaax= x xaxalog
Exponential Equation Method IThis mehod based on “One to One Property”: bM= bNif, and only if M = N•Write each side as a power of the same base•Then set exponents = and solve.
Example:Solve 27x+3= 9x-1
Example:Solve 27x+3= 9x-1•Solution:33x+9= 32x-2Now we can set the exponents = since bases are equal:3x +9 = 2x -2Sub 2x and 9 both sidesx = -11
Solve Exponential Equations Using Natural Logarithms1.Isolate the exponential expression on one side2.Take natural logarithm of both sides of equation3.Simplify using properties like ln bx= x ln b or ln ex= x4.Solve for the variable