
Junior Member
Solve for x: e^2x  e^x  6 = 0
Solve for x with exact values (no decimals):
e^(2x)  e^x  6 = 0
I know how to generally solve this problem  by changing it to quadratic form:
(e^x  3)(e^x + 2)=0
And seeing that:
e^x = 3
and
e^x = 2 (though this one is not possible)
So i'm left with e^x = 3. Ln both sides:
xln(e) = ln(3)
x = ln(3)
But I can't do it this way since solving ln(3) would require a calculator (and a huge number of decimals no less)
Is there another trick to solving problems such as this for exact values? Thanks
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