Question #d1ddf

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Answer 1 · 2017-03-22T10:38:16

$y = 1.4434035067785973$

$(4y)^y -8^(5y-6)=0$

$2^(2y)y^y=2^(3(5y-6))=2^(15y)2^(-18)$

simplifying

$y^y=2^(13y)2^(-18)$

or

$(y/2^13)^y=2^(-18)$

Calling now $z=y/2^(13)$

$z^(2^(13)z)=(z^z)^(2^13)=2^(-18)$

or

$z^z = 2^(-18/(2^13))$

giving

$z=z_0=log(a)/(W(log(a)))=0.00017619671713605924$

with $a=2^(-18/(2^13))$

where $W(z)=ze^z$ is the so called Lambert function.

and finally

$y = 2^(13) xx 0.00017619671713605924=1.4434035067785973$