#### Transcript 10.3 – 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 + logbn Ex. • Product Property: logbmn = logbm + logbn Ex. log95x • Product Property: logbmn = logbm + logbn Ex. log95x = log95 • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m n • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm n • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x 9 • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x 9 • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp = plogbm • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp = plogbm • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp = plogbm Ex. • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp = plogbm Ex. log9x7 • Product Property: logbmn = logbm + logbn Ex. log95x = log95 + log9x • Quotient Property: logb m = logbm - logbn n Ex. log9 x = log9x – log99 9 • Power Property: logb mp = plogbm Ex. 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 4 x3 = 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 x3 = 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 4 x3 = 16 4 x3 = 64 x=4 b. log4 x – log4 (x – 6) = 2 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 Change to exponential form!!! b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x 1 x–6 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 16(x – 6) = x b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 16(x – 6) = x 16x – 96 = x b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 16(x – 6) = x 16x – 96 = x 15x = 96 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15 b. log4 x – log4 (x – 6) = 2 log4 x = 2 x–6 42 = x x–6 16 = x x–6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15 x = 32/5