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Properties of Logarithms
Logarithmic functions with respect to base 'e' are called natural logarithmic functions and are expressed as y = logex. 'logex' is commonly written as 'ln x'. Thus 'ln x' is the power to which 'e' must be raised to get x.
The relationship between natural logarithm and logarithm with respect to any base other than 'e' is:
logex = logax . logea
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
degree of a diffrential equation
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how does proportionality work
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