# LN¶

 Syntax LN (x) Location QL ROM

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.

CROSS-REFERENCE

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.