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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
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If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
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Utilizes the definition of the limit to prove the given limit. Solution Let M > 0 be any number and we'll have to choose a δ > 0 so that, 1/ x 2 > M
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