LogarithmDate: 4/6/96 at 22:41:35 From: Anonymous Subject: Logarithm How to solve this question? LOG 2 156 Date: 7/31/96 at 15:7:21 From: Doctor Mike Subject: Re: Logarithm Hello, I assume you mean "log base 2, of 156". Let's just write log for "log base 2", and a^b for a to the power b. Since 2^7=128 and 2^8=256 you know that log(128)=7 and log(256)=8. Because 156 is between 128 and 256, log(156) must be between 7 and 8. My calculator does not do base 2 logs, but it does do natural logs(base = e), so I'll use the relationship log(x)=ln(x)/ln(2). So, log(156) = ln(156)/ln(2) which is 7.2854 approximately. If you want to know why log(x) = ln(x)/ln(2) , here's a proof. It must be shown that 2 to the power ln(x)/ln(2) gives just x. I will be using the important fact that (a^b)^c = a^(b*c). 2^(ln(x)/ln(2)) = (e^ln(2))^(ln(x)/ln(2)) = e^(ln(2)*(ln(x)/ln(2))) = e^ln(x) = x If you have more questions about any part of this answer, please write back to us. Best regards. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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