How many positive real numbers x are there such that xx√x = (x√x)x ?
Options :
A) 1         B) 2         C) 4         D) infinite
I don't know to which chapter it belongs, it's in a book for KVPY

Dear Student,
Please find below the solution to the asked query:

We havexxx=xxxTake log on both sideslogxxx=logxxxxxlogx=xlogxxxxlogx=xlogx32xxlogx=3x2logx2xxlogx=3xlogx2xxlogx-3xlogx=0logx2xx-3x=0xlogx2x-3=0x cannot be 0 as 00 is indeterminatelogx=0 or 2x-3=0x=1 or x=94

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  • 15
I did this like this :
take log both side : log xx√x = log (x.x1/2)x
then :                    x√x log x = x log x3/2
then :                    √x log x = 3/2 log x
then :                    √x = 3/2
then:                      x = + 9/4
So, the answer is coming option (B) which is correct in answer key.
Is my method right, if yes then like it otherwise u can guide me :)
  • 3
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