After all, we need to " guess" to what power we need to raise one number to obtain another. Useful as they are, it may appear that logarithms are difficult to calculate. Also, quite a few physical units are based on logarithms, for instance, the Richter scale, the pH scale, and the dB scale. Outside of mathematics, they're used in statistics (e.g., the lognormal distribution) economy (e.g., the the GDP index), medicine (e.g., the QUICKI index), and chemistry (e.g., the half-life decay). After all, whatever we raise to power 0, we get 1. Whatever the base, the logarithm of 1 is equal to 0. In other words, whenever we write logₐ(b), we require b to be positive. The logarithm function is defined only for positive numbers. They are denoted by ln(x) and log(x) (the second one simply without the small 10), and their bases are, respectively, the Euler number e and (surprise, surprise!) the number 10. There are two very special cases of the logarithm which have unique notation: the natural logarithm and the logarithm with base 10. Just to be on the safe side, let's have the proper, one-sentence logarithm definition highlighted like so:īefore we move further, let us have a pretty bullet list with a few vital points of information about our new friend, the logarithm function. In other words, the two operations return two different values (although both connected to the exponent). On the other hand, the logarithm with base n of n k is k, i.e., Taking the k-th power of a number n means: Just to be on the safe side, let's see an example. The difference is that with the root, it's not an exponential function that we're inverting but a polynomial one. However, we need to be careful here since taking the root can also be considered the inverse of an exponent. The logarithm is the inverse operation to taking an exponent, i.e., the inverse function to the exponential one. And instead of taking the power, we'd like to. Instead of multiplying, we'd like to divide. In other words, often, instead of adding, we'd like to subtract. Useful as they are, it's sometimes useful to have addition, multiplication, and exponent work both ways. And instead of going further, let's stay with this one for a minute. But what if we go one step further and now want to multiply by the same number a few times? Again, there is a new way of writing that – the exponent. This new operation simplifies notation whenever we need to add the same number several times. Soon after we learn the basics of addition, they introduce us to multiplication.
0 kommentar(er)
