math  natural logs
posted by BJ on .
Find the EXACT solution to
e^(1x) = 4^x
You must use logs, not just a calculator.

take ln of both sides
ln( e^(1x) = ln (4^x)
(1x)lne = x(ln4)
1x = 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)