Logarithmic Functions

Logarithmic FunctionsMrs. WhiteAlgebra II

What are logarithms?

•The inverse of the exponential function!

Graph:

http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htm

Definitions of Logarithms

•The logarithmic function is the function , where b is any number such that

• is equivalent to •The function is read "log base b of x".

xy blog

xy blog ybx

103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log416 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 = 1/2 361/2 = 6

log121= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga5 = b ab = 5

logpq = r pr = q

c = logab b = ac

pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log416 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 = 1/2 361/2 = 6

log121= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga5 = b ab = 5

logpq = r pr = q

c = logab b = ac

pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log416 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 = 1/2 361/2 = 6

log121= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga5 = b ab = 5

logpq = r pr = q

c = logab b = ac

pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log416 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 = 1/2 361/2 = 6

log121= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga5 = b ab = 5

logpq = r pr = q

c = logab b = ac

pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log416 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 = 1/2 361/2 = 6

log121= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga5 = b ab = 5

logpq = r pr = q

c = logab b = ac

pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

Change of Base Formula

The Formula

b

vvb log

loglog

Examples

5646.7log

3log3log7

9894.17log

48log48log7

0435.24log

17log17log4

Homework

9.3 Worksheet #3Change of Base Formula