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Logarithm-PreClassWork.pdf

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Department
Physics
Course
PHYSICS 1L03
Professor
Reza Nejat
Semester
Fall

Description
Phys 1L03 Logarithms: A logarithm is an exponent. Logarithm is an opposite of exponential. You may consider logarithms as being inverse of exponential. x If : y = b x is called the logarithm of y with base b. It is written as: logby = x For example: 8 = 2 3 . So 3 is called the logarithm of 8 with base 2. So: log 2 = 3 The logarithm of a positive number, y, with a positive base, b (b ≠1), is defined as the exponent or the power to which the base b is raised to produce the number y. Example: 10000 = 10 4 So log100000 = 4 The logarithm of 10000 with base 10 is 4. 10 is the exponent to which 10 (the base) must be raised to produce 10000. 10 4 = 10000 10 =10000 is called the exponential form log100000 = 4 is called the logarithm form So: log b = x means that y = b x logby = x ⇔ y = b x Take: b = 10 ⇒ log10y = x ⇔ y = 10 x Rules: log bmn) = log m + bog n b (Addition) log ( ) = log m − log n b n b b (Subtraction) log (m ) = nlog m (Power) b b Example: A = (3)×(4) ⇒ log
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