## ramul Group Title how to find x in 4^x+4^(1/x)=8 one year ago one year ago

1. asnaseer Group Title

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

2. ramul Group Title

yes

3. asnaseer Group Title

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

4. ramul Group Title

you can solve algebraically

5. asnaseer Group Title

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 Group Title

then what will be the next step?

7. asnaseer Group Title

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

8. ramul Group Title

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

9. asnaseer Group Title

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 Group Title

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

11. asnaseer Group Title

:) 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 Group Title

13. asnaseer Group Title

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

14. asnaseer Group Title

I left school many many years ago

15. ramul Group Title

on which level are you?

16. asnaseer Group Title

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

17. ramul Group Title

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

18. asnaseer Group Title

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

19. ramul Group Title

done now can you help me?