Section 4 – Logarithmic Functions

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Presentation transcript:

Section 4 – Logarithmic Functions Chapter 11 Section 4 – Logarithmic Functions

Logarithmic Function The logarithmic function y = logax, where a>0, is the inverse of the exponential function y = ax. So, y = logax if and only if x = ay. EX 1: Write in exponential form: 2/3 = log12525 EX 2: Write in exponential form: 1/3 = log82

More Examples Write each equation in logarithmic form. EX 3: 64 = 43

One More Example EX 5: Evaluate the expression log71/49

Properties of Logs PROPERTY DEFINITION EXAMPLE Product logbmn = logbm + logbn log39x = log39 + log3x Quotient logb(m/n)=logbm – logbn log1/4(4/5) = log1/4(4)-log1/4(5) Power logbmp = p(logbm) log28x = x(log28) Power of Equality If logbm = logbn, then m=n log8(3x-4) = log8(5x+2) so, 3x-4 = 5x+2

More Examples EX 6: Solve the equation: logp641/3 = ½ log4(2x+11) = log4(5x-4) EX 8: Solve the equation: log11x + log11(x+1) = log116

Assignment Chapter 11, Section 4 pgs 723-725 #20-52E,60,64