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

Question

asnaseer · Answer

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

anonymous · Answer

yes

asnaseer · Answer

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

anonymous · Answer

you can solve algebraically

asnaseer · Answer

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

anonymous · Answer

then what will be the next step?

asnaseer · Answer

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

anonymous · Answer

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

asnaseer · Answer

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?

anonymous · Answer

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

asnaseer · Answer

:) 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?

anonymous · Answer

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

asnaseer · Answer

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

asnaseer · Answer

I left school many many years ago

anonymous · Answer

on which level are you?

asnaseer · Answer

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

anonymous · Answer

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

asnaseer · Answer

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

anonymous · Answer

done now can you help me?