## anonymous 3 years ago Solve for x: 8^x = 1/6root(2)

1. anonymous

I'm guessing I should change the RHS to (1/2)^(1/6.) Am I right?

2. anonymous

lol tkhunny saves the day again!

3. anonymous

Hello to you as well, sasogeek

4. sasogeek

hi :)

5. 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?

6. anonymous

The latter.

7. anonymous

Sorry. I don't know how to type expressions like this into the field.

8. anonymous

Anyway..I imagine I'm supposed to end up with 2^3^x = (1/2)^(1/6)

9. anonymous

And then 2^3x = 2^(-1/6)

10. 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.

11. anonymous

Alright, will do :). So...is the answer just (-1/6)/2?

12. 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

13. anonymous

Oh...of course. So it's (-1/6)/3, or -1/18

14. anonymous

haha Thank you very much for the medal sasogeek, however undeserved it may be!

15. anonymous

Thank you for all of your help!

16. sasogeek

it is well deserved :) you worked your way through to get the answer ;) and u got it right as well :)

17. anonymous

Well, actually I got it wrong and then tkhunny guided me towards the correct answer, but I'm glad you think so!

18. anonymous

A good night to all!

19. anonymous

Though I'm sure I'll be back.

20. 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 :)

21. anonymous

Well, once again, thank you very much!