Properties of Logarithmic Functions

Objectives: Simplify and evaluate expressions involving logarithms.

Solve equations involving logarithms.

Standard: 2.8.11.N. Solve equations.

Section 6.4

Product and Quotient Properties of Exponents

am • an = am+n Product Property

am/an = am-n Quotient Property

(am)n = am*n Power Property

Product and Quotient Properties of Logarithms

For m > 0, n > 0, b > 0, and b ≠ 1:

Product Property logb (mn) = logb m + logb n

Quotient Property logb (m/n) = logb m – logb n

** Just like the exponent rules!

A. log2 12

= log2 (2 ● 2 ● 3)

= log2 2 + log2 2 + log2 3

≈1 + 1 + 1.5850

≈3.5850

B. log2 1.5

= log2 3/2

= log2 3 – log2 2

≈1.5850 - 1

≈0.5850

C. log 2 18

D. log2 .75

Write each expression as a single logarithm. Then simplify, if possible.

A. log3 10 – log3 5 B. logb u + logb v – logb uw

C. log4 18 – log4 6

D. logb 4x - logb 3y + logb y

Power Property of LogarithmsFor m > 0, b > 0, b ≠ 1, and any real number p:

Ex 3.

logb mp = p logb m

Evaluate log5 254

Log5 254 = 4 log5 25

= 4 ● 2

= 8

Power Property of LogarithmsPower Property of Logarithms

Ex 4.

Evaluate log3 27100

Exponential- Logarithmic Inverse Properties: For b > 0, b ≠1:

logb bx = x and blogb

x = x for x > 0.

A. 3log3

4 + log5 25 B. log2 32 – 5log5

3

C.7log

711 + log381

D.log885 +3log

38

Homework

Integrated Algebra II- Section 6.4 Level A

Honors Algebra II- Section 6.4 Level B