Logs in Different BasesDate: 6/11/96 at 21:40:53 From: Anonymous Subject: Logs in different bases Suppose a and b are positive numbers for which log (a) = log (b) = log (a+2b). Find b/a. 9 15 25 Thanks for your help. - Michael Date: 6/12/96 at 5:53:9 From: Doctor Pete Subject: Re: log problem Here are some hints: Let n = log (a) = log (b) = log (a+2b). 9 15 25 Then 9^n = a, 15^n = b, and 25^n = a+2b. Factoring the bases, we see that 3^(2n) = a, 3^n * 5^n = b, and 5^(2n) = a+2b. Look at these relations carefully, and you will find that you can express two of these in terms of the third, thereby eliminating n. Once you do this, you have a relation in a and b which allows you to find b/a. Another thing to keep in mind: note b/a must be positive; this should eliminate any extraneous solutions you may obtain. -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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