January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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3. ða
x
Þ
y
5 a
xy
. Example: (4
5
)
9
5 4
45
4. a
2x
5 1=a
x
. Example: 4
25
5 1=4
5
5. a
x=y
5
ffiffiffiffiffi
a
x
y
p
. Example: 5
3=7
5
ffiffiffiffiffi
5
3
7
p
2.6 Logarithm
1. log
a
1 5 0; log
a
a 5 1. Example: log
9
1 5 0; log
15
15 5 1
2. log
a
x
m
5 mlog
a
x. Example: log
9
4
2
5 2log
9
4
3. log
a
ðxyÞ5 log
a
x 1 log
a
y. Example: log
9
ð7 3 18Þ5 log
9
7 1 log
9
18
4. log
a
ðx=yÞ5 log
a
x 2 log
a
y. Example: log
9
ð7=18Þ5 log
9
7 2 log
9
18
5. log
a
x 5 log
a
b log
b
x. Example: log
9
ð7Þ5 log
9
15 log
15
7
6. log
a
x 5
log
b
x
log
b
a
Note: From (5), taking x 5 a; we get the formula:
log
a
b 5
1
log
b
a
: Example: log
9
18 5
1
log
18
9
2.7 Factorials
The factorial of positive integer n is the product of all positive integers less than or
equal to the integer n and is
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