7.4 P ROPERTIES OF L OGARITHMS

R EVIEW : P ROPERTIES OF E XPONENTS

P RODUCT P ROPERTY The logarithm of a product is equal to the sum of the logarithms of the factors. Example: log = log 3 (27 * 27) = log log 3 27 log b mn = log b m + log b n

Q UOTIENT P ROPERTY OF L OGARITHMS The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor log 4 (16 ÷ 2) = log 4 16 – log 4 2 log b (m÷n) = log b m – log b n

P OWER PROPERTY OF L OGARITHMS Let’s try this one: log 10 3 (use the product property. log b a p = p log b a

I NVERSE P ROPERTY OF L OGARITHMS How do you solve something like 2x – 5 = 9? Use inverse operations. So, how do you “undo” a log? An exponential? log b b x = xb log b x = x

S OME PROBLEMS Simplify: log log 2 (8x) log 8 8 3x+1

C HANGE OF B ASE F ORMULA

E XPRESS AS A SINGLE LOGARITHM. S IMPLIFY, IF POSSIBLE. log log log log 1000 log log 3 27

S IMPLIFY AND EVALUATE log – log 4 5 log 5.4 – log log – log 6 2.3

S IMPLIFY log log log log 1/2 (0.25) 4

S IMPLIFY log 2 2 x log log log 2 (0.5) 4

E VALUATE log 9 (1/27) log 8 32 log 5 10 log 2 27