S.O.S. Mathematics CyberBoard

e^4x+4e^2x-21=0
I think I'm supposed to substitute u=e^2x so then i got u=either -7 or 3 but where do I go from there?

The -7 does not correspond to a real root. You can take logs to solve for the other root.

_________________
Live long and prosper.

so solve for 3 and not -7?

It depends on what grade you are in. If you have been exposed to complex numbers, you need both. Otherwise solution for 3 will do.

This is the algebra forum, not the analysis forum. CONTEXT.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

That is a strange assertion. Complex numbers are usually introduced into algebra courses, once you are trying to solve x^2 + 1 = 0.

But solving for values of the exponential which give negative values comes from Euler's formula, introduced in a precalculus or calculus, not in algebra.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

I have no expertize on math curricula. In my student days, there was no such thing as "precalculus". What I took (senior year in high school) was called "advanced algebra". I suspect it covered the same material, including Euler's formula.

I suspect that is where our disconnect is then, a standard senior level class does cover such things, but in the form of "precalculus [and trig]", rather than the second algebra class which -- though they do briefly introduce complex numbers -- does not deal with them very thoroughly, and certainly not at the level of Euler's formula.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination