Question 468400
2e^2x+5e^x-12=0 
Apparently the answer is (ln3)/2. I'm not sure why it's not ln(3/2) or even ln3-ln2=ln1=0. An explanation would be so very much appreciated!
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2e^2x+5e^x-12=0
let x=e^x
x^2=e^2x
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2x^2+5x-12=0
(2x-3)(x+4)=0
x=3/2
 or
x=-4
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e^x=-4 (reject, e^x>0)
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e^x=3/2
xlne=ln(3/2)
x=ln(3/2) (ans)
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I don't know how they got answer you found, ln(3)/2