8.5 – Using Properties of Logarithms

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    16-Jan-2016
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8.5 – Using Properties of Logarithms. Product Property:. Product Property: log b mn. Product Property: log b mn = log b m. Product Property: log b mn = log b m + log b n. Product Property: log b mn = log b m + log b n Ex. Product Property: log b mn = log b m + log b n Ex. log 9 5 x. - PowerPoint PPT Presentation

Transcript of 8.5 – Using Properties of Logarithms

  • 8.5 Using Properties of Logarithms

  • Product Property:

  • Product Property: logbmn

  • Product Property: logbmn = logbm

  • Product Property: logbmn = logbm + logbn

  • Product Property: logbmn = logbm + logbnEx.

  • Product Property: logbmn = logbm + logbnEx. log95x

  • Product Property: logbmn = logbm + logbnEx. log95x = log95

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9x

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property:

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m n

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm n

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn n

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx.

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x 9

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x 9

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property:

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp = plogbm

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp = plogbm

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp = plogbmEx.

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp = plogbmEx. log9x7

  • Product Property: logbmn = logbm + logbnEx. log95x = log95 + log9xQuotient Property: logb m = logbm - logbn nEx. log9 x = log9x log99 9Power Property: logb mp = plogbmEx. log9x7 = 7log9x

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16 log5 x3 = log5 16 4

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16 log5 x3 = log5 16 4

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16 log5 x3 = log5 16 4x3 = 16 4

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16 log5 x3 = log5 16 4x3 = 16 4 x3 = 64

  • Ex. 2 Solve the following equations.a. 3 log5 x log5 4 = log5 16 log5 x3 log5 4 = log5 16 log5 x3 = log5 16 4x3 = 16 4 x3 = 64 x = 4

  • b. log4 x log4 (x 6) = 2

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 Change to exponential form!!!

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = x 1 x 6

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6 16(x 6) = x

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6 16(x 6) = x16x 96 = x

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6 16(x 6) = x16x 96 = x15x = 96

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6 16(x 6) = x16x 96 = x15x = 96 x = 96/15

  • b. log4 x log4 (x 6) = 2 log4 x = 2x 6 42 = xx 6 16 = xx 6 16(x 6) = x16x 96 = x15x = 96 x = 96/15 x = 32/5