LN (x)



This function returns the natural logarithm of the given value (in base e), so that eLN(x)=x. Due to the nature of power numbers, the range of x is 0>x<=22046.

Logarithms were first invented to make multiplication and division easier, because whatever base you are working in, multiplication and division can be calculated by using logarithms. For example, x*y is the same as EXP(LN(x)+LN(y)), or 10(LOG10(x)+LOG10(y)); and x/y is the same as EXP(LN(x)-LN(y)), and 10(LOG10(x)-LOG10(y)).

Another reason is that logarithms can make it easier to calculate powers, for example, 10(p*LOG10(y)) gives the same answer as yp, for any value of y or p.

Another use for logarithms is to enable square roots to be calculated. On the assumption that x*x=10(2*LOG10(x)), the square root of a number y can be calculated using the formula: 10(LOG10 (y) / 2).

Natural logarithms (base e) are generally used in theoretical mathematics, as this can be useful in differentiation, since if y=ex, dy<dx<y. Because negative values of x cannot be handled by logarithms (in any base - this is because xy must always be greater than zero!), you will need to check for negative values and zero values separately.


EXP converts natural logarithms to their true numbers in base 10, LOG10 provides logarithms in base 10 (common logarithms), and LOG2 provides base 2 logarithms.