Chris Berry wrote:
Mark Lane wrote:I was a math major in a former life 10+ years. 1/2(e^x + e^-x) = 4 e^x + e^-x = 8 (e^x)^2 + 1 = 8e^x Let y = e^x such that x = ln(y). y^2 + 1 = 8y y^2 - 8y + 1 = 0Use quadratic formula, which is x = (-b +- sqrt(b^2 - 4ac))/2a, to solve fory in previous equation. Then x = ln(y)Pretty, but pure handwaving, you still didn't provide a value for x.
To continue the handwaving some more then :)Using the quadratic formula and keeping only the positive value for y (y = e^x - as such y cannot be negative!) we get:
y = (8 + 9.592) /2 = 8.796 This means e^x = 8.796 => x = ln(8.796) = 2.174 -- --Moby They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. -- Benjamin Franklin First they came for the Jews and I did not speak out because I was not a Jew. Then they came for the Communists and I did not speak out because I was not a Communist. Then they came for the trade unionists and I did not speak out because I was not a trade unionist.Then they came for me and there was no one left to speak out for me. -- Pastor Martin Niemöller
***************************** New Site from The Kenzig Group!Windows Vista Links, list options and info are available at:
mode or view archives use the below link. http://thethin.net/win2000list.cfm