Question

resolva a equação ln(x/2)=lnx/ln2

a)x=ln²2 b)x= e^ln²2/2-ln2

c)x= e^ln²2/ln2-1 d)vale para todo x>0

Answer 1

ln(x/2) =lnx/ln2
ln2 . ln(x/2) = lnx
ln2(lnx - ln2) = lnx
ln2.lnx - ln²2 = lnx
ln2.lnx - lnx = ln²2
lnx(ln2 - 1) = ln²2
lnx = ln²2/(ln2 - 1)
x = e^ln²2/(ln2-1)

Letra C

Answer 2

ln(x/2) = lnx/ln2

lnx - ln2 = lnx / ln2

ln2 * lnx - ln2 * ln2 = lnx

ln2 * lnx - lnx = ln²2 

lnx (ln2 - 1) = ln²2

lnx = ln²2 /(ln2 - 1)

e^(lnx) = e^[ln²2 /(ln2 - 1)]

x = e^[ln²2/(ln2 - 1)]

Alternativa (C)

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09/03/2016
Sepauto - SSRC
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