LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

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Presentation transcript:

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6

SOLVING LOGARITHMIC EQUATIONS EXAMPLES: EXAMPLES: Solve log 3 (4x - 7) = 2 Solve log 3 (4x - 7) = 2 Solve 2 log 5 x = log 5 9 Solve 2 log 5 x = log 5 9 Solve log 4 (x + 3) + log 4 (2 - x) = 1 Solve log 4 (x + 3) + log 4 (2 - x) = 1

SOLVING EXPONENTIAL EQUATIONS Solve:e x = 2 Take ln of both sides ln e x = ln 2 Take ln of both sides ln e x = ln 2 x.6931

SOLVE EXPONENTIAL EQUATIONS 3  4 2X - 5 = 20 3  4 2X - 5 = X - 5 = 20/3 4 2X - 5 = 20/3 log 4 2X - 5 = log (20/3) log 4 2X - 5 = log (20/3) (2x - 5)log 4 = log (20/3)

SOLVE EXPONENTIAL EQUATIONS 2x - 5 = x = x = x =

SOLVING LOGARITHMIC EQUATIONS EXAMPLES: EXAMPLES: Solve 3 x + 1 = 81 Solve 3 x + 1 = 81 Solve 4 x - 2 x - 12 = 0 Solve 4 x - 2 x - 12 = 0 Solve 2 x = 5 Solve 2 x = 5 Solve 8  3 x = 5 Solve 8  3 x = 5 Solve 5 x - 2 = 3 3x + 2 Solve 5 x - 2 = 3 3x + 2

CONCLUSION OF SECTION 4.6 CONCLUSION OF SECTION 4.6