# 8.5 – Using Properties of Logarithms

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16-Jan-2016Category

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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