how to find x in 4^x+4^(1/x)=8

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how to find x in 4^x+4^(1/x)=8

Mathematics
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is the 2nd term definitely \(4^{\frac{1}{x}}\) and not \(4^{-x}\)?
yes
have you been asked to use any specific methods? e.g. solve algebraically or numerically?

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Other answers:

you can solve algebraically
I can see one answer just by observation. See if you can also spot it if you rearrange your equation as:\[4^x+4^{\frac{1}{x}}=4+4\]
then what will be the next step?
observe the equation carefully - the answer should just "jump out" :)
on which basis rearrangement is done? can it be done to solve the equation?
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?
actually is this legal process? is any other method is there?
:) 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?
can you ask this to any of your teacher (maths)?
I am not in school - I do maths as a hobby so I have no teacher as such :)
I left school many many years ago
on which level are you?
I studied Aeronautical Engineering when I was at University. I now work as a software engineer
i want to ask next question how to prove null set is subset of every set ?
<--- you should ask each question separately in the list to the left. you can do this by first closing this question.
done now can you help me?

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