if 2^{x^{\cos(x)}}\sqrt{\cos(x)}=2^x x>0 and \cos(x)>0 what does x equal in 2^x=2^{1.5} exactly?

Terrence Moore

Terrence Moore

Answered question

2022-04-21

if 2xcos(x)cos(x)=2x
x>0 and cos(x)>0
what does x equal in 2x=21.5 exactly?

Answer & Explanation

kayuukor9c

kayuukor9c

Beginner2022-04-22Added 13 answers

Part One:
2x=21.5x=1.5
Take the natural logarithm of both sides to see this.
Part Two:
f(x)=2xcos(x)cos(x)2x
Because 0<cos(x)1, we know that
2xcos(x)cos(x)2x
And equality is achieved where x is a multiple of 2π
So your solutions are x=2nπ for n1

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