Find the EXACT solution to

Question

e^(1-x) = 4^x

You must use logs, not just a calculator.

Answer 1

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)