Elenathehomeschooler
  • Elenathehomeschooler
can someone help me solve for x e^x e^(x+1)=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Ms-Brains
  • Ms-Brains
Is this all of your question?
Elenathehomeschooler
  • Elenathehomeschooler
\[e^x e ^{x+1} =1\]
Elenathehomeschooler
  • Elenathehomeschooler
yes

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Ms-Brains
  • Ms-Brains
What do you think it is?
zepdrix
  • zepdrix
Recall your exponent rule:\[\large\rm a^b\cdot a^c\quad=a^{b+c}\]
zepdrix
  • zepdrix
Do you see how that will help us on the left side of the equation?
Elenathehomeschooler
  • Elenathehomeschooler
yes
Elenathehomeschooler
  • Elenathehomeschooler
i think it might be 0
zepdrix
  • zepdrix
For x? Hmm no.
zepdrix
  • zepdrix
Applying the rule to the left side gives us:\[\large\rm e^{x+(x+1)}=1\]\[\large\rm e^{2x+1}=1\]Then apply natural log to each side. Or rewrite 1 as e^0. Whichever method you prefer
zepdrix
  • zepdrix
\[\large\rm e^{2x+1}=e^0\]
Elenathehomeschooler
  • Elenathehomeschooler
would we cancel out e
zepdrix
  • zepdrix
Bases are equivalent, both e, so the exponents must be equivalent as well, ya? :) \[\large\rm 2x+1=0\] Sure, you can think of it as cancelling out, ya
Elenathehomeschooler
  • Elenathehomeschooler
would we get -0.5
zepdrix
  • zepdrix
Yes :)
Elenathehomeschooler
  • Elenathehomeschooler
yay! so the answer is x=-0.5
zepdrix
  • zepdrix
yay good job
Elenathehomeschooler
  • Elenathehomeschooler
Thank you so much!

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