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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?

you can solve algebraically

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?

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

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 ?

done now can you help me?