Homework Help: math - natural logs

Posted by BJ on Monday, October 31, 2011 at 10:10pm.

Find the EXACT solution to
e^(1-x) = 4^x

You must use logs, not just a calculator.

math - natural logs - Reiny, Monday, October 31, 2011 at 10:15pm
take ln of both sides

ln( e^(1-x) = ln (4^x)
(1-x)lne = x(ln4)
1-x = xln4
xln4 + x = 1
x(ln4 + 1) = 1
x = 1/(ln4 + 1)
= appr. .419

check
LS = e^.581 = 1.7877
RS = 4^.416 = 1.7877 (not bad)

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