anonymous
  • anonymous
e^x4=1000
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
to cancel out e you have to take the ln to both sides\[\ln( e ^{(4*x)})=ln(1000)\] \[{(4*x)}=ln(1000)\] \[{(x)}=(ln(1000))/4\]
anonymous
  • anonymous
I thought I had to 4th root each side because I am left with x^4=ln1000?
anonymous
  • anonymous
Am I wrong?

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anonymous
  • anonymous
its xto the 4th not 4*x?
anonymous
  • anonymous
What is the original equation? a) \(e^{x^4} = 1000\) b) \(e^{x4} = 1000\) c) \(e{x^4} = 1000\)
anonymous
  • anonymous
a
anonymous
  • anonymous
Ok, so start by taking the natural log of both sides.
anonymous
  • anonymous
You can't take the 4th root yet because you'd have \[(e^{x^4})^{\frac{1}{4}} = e^{\frac{x^4}{4}} \]
anonymous
  • anonymous
\[e ^{x ^{4}} = 1000\] so \[ln(e ^{x ^{4})} = ln(1000)\] \[{x ^{4}} = ln(1000)\] \[x= \sqrt[4]{\ln(1000)}\] or you can say \[x= (\ln(1000))^{1/4}\]
anonymous
  • anonymous
It wouldn't get rid of the power of 4 on the x.
anonymous
  • anonymous
Is there an answer to this or is that it?? I am so confused?
anonymous
  • anonymous
Romero is correct. The answer is the \[x=\sqrt[4]{ln\ 1000}\]
anonymous
  • anonymous
do I type that into my caculator to get an answer??
anonymous
  • anonymous
sure, or you can leave it that way.
anonymous
  • anonymous
What would the answer be if I typed it into my caculator. I am new to this scientific....is it 10.5130????
anonymous
  • anonymous
I have 1.6211
anonymous
  • anonymous
err 1.62119 rather.
anonymous
  • anonymous
Thank you.. with that answer I was able to figure out which buttons to press on this caculator... its going to be the death of me...!!

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