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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#