# 8.5 – Using Properties of Logarithms. Product Property:

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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

Ex.

Product Property: log b mn = log b m + log b n Ex. log 9 5x

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property:

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m n

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m n

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex.

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x 9

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x 9

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property:

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p = plog b m

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p = plog b m

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p = plog b m Ex.

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p = plog b m Ex. log 9 x 7

Product Property: log b mn = log b m + log b n Ex. log 9 5x = log 9 5 + log 9 x Quotient Property: log b m = log b m - log b n n Ex. log 9 x = log 9 x – log 9 9 9 Power Property: log b m p = plog b m Ex. log 9 x 7 = 7log 9 x

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16 log 5 x 3 = log 5 16 4

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16 log 5 x 3 = log 5 16 4

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16 log 5 x 3 = log 5 16 4 x 3 = 16 4

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16 log 5 x 3 = log 5 16 4 x 3 = 16 4 x 3 = 64

Ex. 2 Solve the following equations. a. 3 log 5 x – log 5 4 = log 5 16 log 5 x 3 – log 5 4 = log 5 16 log 5 x 3 = log 5 16 4 x 3 = 16 4 x 3 = 64 x = 4

b. log 4 x – log 4 (x – 6) = 2

log 4 x = 2 x – 6

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 Change to exponential form!!!

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x 1 x – 6

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6 16(x – 6) = x

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6 16(x – 6) = x 16x – 96 = x

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15

b. log 4 x – log 4 (x – 6) = 2 log 4 x = 2 x – 6 4 2 = x x – 6 16 = x x – 6 16(x – 6) = x 16x – 96 = x 15x = 96 x = 96/15 x = 32/5