Re: Beyond Don's charts?
From Stanford Wong's BJ21
Posted by Don Schlesinger on 1 Oct 1997, at 10:33 a.m., in response to Re: Beyond Don's charts?, posted by truefive on 1 Oct 1997, at 9:12 a.m.
"Please straighten me out on one value in each equation that I don't understand. In the first it's "ln" (I think that's a lower case letter "l" and not a numeral one). I believe r represents the risk, which in your example is 10%, so that would make ln = -23, but I can't figure out what this is and consequently don't know what value to plug in for future use."
Sorry for any confusion. "Ln" stands for the "natural logarithm" (now there's a big help!). Logarithms are used in mathematics to help us with some calculations that, otherwise, could be quite tedious. So, the short answer is: use a scientific calculator that has a "ln" button and simply enter .10 and hit the button. It will return -2.3 as the answer, because the natural log of .10 is -2.3.
To understand why, I'm afraid you need to understand what a log (short for "logarithm") is, and what the next term you're asking about, the letter e, has to do with all of this.
The dictionary defines "logarithm" as: "the exponent of the power to which a base number must be raised to equal a given number." So, if I use the number 10 as the base of my log system, then the log of 100 is 2, because 2 is the power to which I must raise 10 in order to equal 100.
Now, in another system, the base is not 10, but rather the number "e." (I know it's funny to call it a number; but think of pi = 3.1416. We sometimes designate numbers by letters.) It turns out that e is approximately equal to 2.7183. Now, when we ask for the ln of .10, we're asking "to what power must e (2.7183) be raised such the answer is .10? It turns out that the answer is -2.3.
You can see this from the charts on p. 167 of "BJA" where, unfortunately, the column headings were inadvertently omitted. For Table 9.7, the headings are, respectively, x, e^x and e^-x, and these are repeated to the right. So, to find e^-2.3, go to the far-most right-hand column, near the top, on the 2.30 line. We read the answer as 0.1003, or roughly, 10%.
I suspect this is much more than you really wanted to know! If you can simply apply the formulas and use the numbers that they provide, it really isn't necessary to understand the theoretical math.
Hope this helps.
"In the second equation it's "e". I see that E (in BJA, not above, where you use ev) is = to ev but I can't figure out lower case e. I tried using the ev again in case there was no difference but it didn't provide the right answer."
See above.
Don