Properties of Logarithmic Functions

Objectives: Simplify and evaluate expressions involving logarithms.

Solve equations involving logarithms.

Standard: 2.8.11.N. Solve equations.

Warm-Up:7z 12t 3c

3

3

mn

6 6a b 8 4r s

John Napier is most remembered as the inventor of logarithms and Napier's bones, and for popularizing the use of the decimal point. Napier's birth place, Merchiston Tower, Edinburgh, Scotland, is now part of Edinburgh Napier University. After dying of gout, Napier was buried in St Cuthbert's Church, Edinburgh.

Properties of Exponents

Product Property

Quotient Property

Power Property

TRY THIS, top of 379

2log (2 3 3)

2 2 2log 2 log 3 log 3

l 1.5850 1.5850

4.17

2 2log 3 log 4

1.5850 2

0.415

TRY THIS - middle of p. 379

418log6

4log 3

4log log3b bx yy

4log3bxyy

4log3bx

page 381 #5-8

TRY THIS – top of p. 380

3100 log 27

3

3

log 273 27

3 33

x

xx

x

3100 log 27100 3300

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

TRY THIS – Bottom of 380

11 47

5 813

p. 381 #9-11

p. 381 #12

p. 382: #30-36 even

p. 382: #44, 46, 48, 56

HOMEWORK: Practice 6.4

Quiz on 6.1 – 6.4: Fri Apr 23