anonymous
  • anonymous
Solve for x: 8^x = 1/6root(2)
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
I'm guessing I should change the RHS to (1/2)^(1/6.) Am I right?
anonymous
  • anonymous
lol tkhunny saves the day again!
anonymous
  • anonymous
Hello to you as well, sasogeek

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sasogeek
  • sasogeek
hi :)
tkhunny
  • tkhunny
First, I'm not clear on your notation. Is it \(8^{x} = \dfrac{1}{6}\sqrt{2}\) or maybe \(8^{x} = \sqrt[6]{2}\) or something else?
anonymous
  • anonymous
The latter.
anonymous
  • anonymous
Sorry. I don't know how to type expressions like this into the field.
anonymous
  • anonymous
Anyway..I imagine I'm supposed to end up with 2^3^x = (1/2)^(1/6)
anonymous
  • anonymous
And then 2^3x = 2^(-1/6)
tkhunny
  • tkhunny
No worries. Learning just a little LaTeX can go a long way. You just have to find other ways to communicate without it. Click the [Equation] button, below, and do some experimenting.
anonymous
  • anonymous
Alright, will do :). So...is the answer just (-1/6)/2?
tkhunny
  • tkhunny
Excellent! 2^(3x) is the real key to this problem's simplest solution. Same bases! If they are to be equal, the exponents must be equal. 3x = -1/6 if we started with \(\dfrac{1}{\sqrt[6]{2}}\) or 3x = 1/6 if we started with \(\sqrt[6]{2}\) or
anonymous
  • anonymous
Oh...of course. So it's (-1/6)/3, or -1/18
anonymous
  • anonymous
haha Thank you very much for the medal sasogeek, however undeserved it may be!
anonymous
  • anonymous
Thank you for all of your help!
sasogeek
  • sasogeek
it is well deserved :) you worked your way through to get the answer ;) and u got it right as well :)
anonymous
  • anonymous
Well, actually I got it wrong and then tkhunny guided me towards the correct answer, but I'm glad you think so!
anonymous
  • anonymous
A good night to all!
anonymous
  • anonymous
Though I'm sure I'll be back.
sasogeek
  • sasogeek
sure he did :) and that was great of him/her lol but at the end of the day, i think you deserve the medal for your effort :)
anonymous
  • anonymous
Well, once again, thank you very much!

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