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## ramul 3 years ago how to find x in 4^x+4^(1/x)=8

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1. asnaseer

is the 2nd term definitely $$4^{\frac{1}{x}}$$ and not $$4^{-x}$$?

2. ramul

yes

3. asnaseer

have you been asked to use any specific methods? e.g. solve algebraically or numerically?

4. ramul

you can solve algebraically

5. asnaseer

I can see one answer just by observation. See if you can also spot it if you rearrange your equation as:$4^x+4^{\frac{1}{x}}=4+4$

6. ramul

then what will be the next step?

7. asnaseer

observe the equation carefully - the answer should just "jump out" :)

8. ramul

on which basis rearrangement is done? can it be done to solve the equation?

9. asnaseer

try and equate the $$4^x$$ with the first 4 on the right-hand-side. Similarly try and equate the $$4^{1/x}$$ with the second 4 on the right hand side. What value of x satisfies both?

10. ramul

actually is this legal process? is any other method is there?

11. asnaseer

:) I'm not sure if it is a "legal" mathematical proof or not, but that is the method I used. Maybe others can come up with alternatives?

12. ramul

can you ask this to any of your teacher (maths)?

13. asnaseer

I am not in school - I do maths as a hobby so I have no teacher as such :)

14. asnaseer

I left school many many years ago

15. ramul

on which level are you?

16. asnaseer

I studied Aeronautical Engineering when I was at University. I now work as a software engineer

17. ramul

i want to ask next question how to prove null set is subset of every set ?

18. asnaseer

<--- you should ask each question separately in the list to the left. you can do this by first closing this question.

19. ramul

done now can you help me?

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