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
bvvb log
loglog
Examples
5646.7log3log3log7
9894.17log48log48log7
0435.24log17log17log4
Homework9.3 Worksheet #3Change of Base Formula