Logaxy = loga x + loga y
Example:
Log4 (2*32) = Log464 = log4 2 + log4 32
=
loga x - loga y
Example:
=
log3 81 – log3 27 = 4 – 3 = 1
Logaxr = rlogax
Example:
Log482 = 2log48
LOGARITHMS
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Exponential Form: x = by
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Example: |
8 = 23
|
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Logarithmic Form: y = logb x
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Example: |
3 = log2 8
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b > 0
Common Logarithms: Logarithms with base 10. b = 10
Logarithm of a negative number is not defined. Example: log2 (-8) is undefined.
Basic Properties of Logarithms:
|
logb 1 = 0
|
Example: |
Log3 1 = 0
|
30 = 1 |
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logb b = 1
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Example: |
Log3 3 = 1
|
31 = 3 |
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logb bx = x
|
Example: |
Log3 34 = 4
|
34 = 34
|
|
blogbx = x
|
Example: |
3log34 = 4
|
Log3 4 = log3 4 |
Properties of Logarithms:
|
Logaxy = loga x + loga y |
Example: |
Log4 (2*32) = Log464 = log4 2 + log4 32 |
|
|
Example: |
|
|
Logaxr = rlogax |
Example: |
Log482 = 2log48 |
Change of Base Formulas:
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