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Science & Mathematics by Anonymous 2018-06-29 01:32:58
Social Science
Why are these two equations giving different answers?
1 answer
e^2x-4e^x=5 solving for x yields ln5 now, shouldn't ln(e^2x) - ln(4e^x) = ln5 yield ln5? When I solved this the answer was ln20, why are the answers different? Isn't it acceptable to take the natural log of both sides of an equation?
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Anonymous
e^(2x)-4e^x-5=0 => (e^x)^2-4(e^x)-5=0 => (e^x-5)(e^x+1)=0 => e^x=5 or e^x=-1 for real solution, e^x=5 => xln(e)=ln(5) => x=ln(5) Note that e^(2x)-4e^x=5 can not be replaced by ln[e^(2x)]-ln(e^x)=ln(5). The answer x=ln(20) is not correct.
