Question

why does 2^(log4(n))= sqrt (n)?

Answer 1

*
That is log base 4 of n

Answer 2

Here's a hint to get you started:

Assume that it is true and square both sides and see if you can get to something you know absolutely to be true. If you can, then you know that if you had to, you could work backwards to get to this equality.

So, square both sides? What do you get? Show all your work.

Answer 3

Alright let me see what happens

Answer 4

wouldn't I get 2^(2logn/log4)=n

Answer 5

\[\LARGE{2^{\log_{4}n } \times 2^{\log_{4}n } = \sqrt{n} \times \sqrt{n}}\]\[\LARGE{2^{2 \times \log_{4}n } = n}\]\[\LARGE{4^{\log_{4}n } = n}\]\[\LARGE{n = n}\]

Answer 6

So, obviously,

n = n

So, if we wanted to, we could always reverse these steps and arrive at the orig. So, that's all you have to do.

Answer 7

So x^logx(k)= k?

Answer 8

Yes, and that's really the whole key to this and why we chose to work "backwards". When you think about it, log x(k) is the exponent that, once you put it on x, you get k. So, when you put that on x, you simply get k.

Answer 9

Cool thank so much!

Answer 10

Good luck to your studies and thanks for the recognition! @artmilko

Answer 11

And you're welcome!

Answer 12

Have a good one :)

Answer 13

That is, "good luck to you in all of your studies" Openstudy is chopping off my words again!