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LOGS and LN and e

LOGS and LN and e. 11 2x = 102 x-1 Log 11 2x = log 102 x-1 2x Log 11= (x-1) log 102 use distrib. Prop. 2x log 11 = x log 102 - log 102 group x -x log 102 - xlog 102 2x log 11 – x log 102 = -log 102 factor out x x(2 log 11 -log 102) = -log 102 divide.

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LOGS and LN and e

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  1. LOGS and LN and e

  2. 112x = 102x-1 Log 112x= log 102x-1 2x Log 11= (x-1) log 102 use distrib. Prop. 2x log 11 = x log 102 - log 102 group x -x log 102 - xlog 102 2x log 11 – x log 102 = -log 102 factor out x x(2 log 11 -log 102) = -log 102 divide _______________ (2 log 11 log 102) _______________ (2 log 11 -log 102)

  3. 72x = 35x-2 Log 72x = log 35x-2 2x Log 7= (5x-2) log 3 use distrib. Prop. 2x log 7 = 5x log 3 – 2 log 3 group x -5x log 102 - 5x log 3 2x log 7 – 5x log 3 = -2 log 3 x(2 log 7 – 5 log 3) = -2 log 3 _______________ (2 log 7 – 5 log 3) _______________ (2 log 7 – 5 log 3)

  4. (ln x)2 – 5 ln x + 6 = 0 ( Ln x – 3) ( ln x – 2) = 0 ln x - 3 =0 or ln x -2 = 0 +3 +3 +2 +2 ln x=3 ln x=2 x=e3 x=e2 e e

  5. ex = 72x-3 ln ex = ln 72x-3 x ln e = (2x-3) ln 7 x ln e = 2x ln 7 – 3 ln 7 -2x ln 7 -2x ln 7 x ln e – 2x ln 7 = -3 ln 7 x (ln e – 2 ln 7) = -3 ln 7 ___________ (ln e – 2 ln 7) ___________ (ln e – 2 ln 7)

  6. Change of base formula • Log8 5 = • F(x)= log 6 x =

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