logarithms and natural logarithms

If a > 0 such that a y = x then y is called the logarithm of x with respect to the = base ‘a’ and written as log a x = ..

We know that log 2 8 is the number to which 2 must be raised to get 8. Therefore, log 2 8 = 3. In general, if a x = y, (a > 0), then we say that log a y = x. If e x = y, then we say that the natural logarithm of y is x and we write log y = x. In other words, if the base of a ..

Logarithmic Series - If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x). If x is a real number such that |x|<1, then the series is c..

If x is a real number such that |x|<1, then the series is called the logarithmic series. It can be proved mathematically that this logarithmic series has the sum equal to log(1 + x..

Logarithmic function is f (x) = log x. Its graph i..

When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x) g(x) Taking log on both sides, we have logy = g(x) logf(x). Differentiating with respect to x, we get, ..

Let z= x + iy be a complex number. Let Z = r i q . This formula is useful for finding the logarithm of negative numbers als..

To find the logarithm of a Complex number - Let z= x + iy be a complex number. Taking log on both side..

For any number x such that |x|<1. i) For number x:|x|<1, we have |-x|=|x|<1. iii) It can be proved mathematically that the logarithmic series (1) is true even when x=1..

Summary Exponential and Logarithmic Series - 2 < e < 3 The value of e rounded off to four decimal places is 2.7183. For complex numbers x,y, we have e x + y = e x y y . For any rational number x, the sum, e x , of the seri..