Solve #((4y)/8^5)^y = 8^-6# ?

1 Answer
Apr 16, 2017

#y = 1.4434#

Explanation:

Manipulating the original equation after doing #z = (4y)/8^5# we arrive at

#z^((8^5/4)z)=8^-6# or

#(z^((8^5/4)z))^(4/8^5)=(8^-6)^(4/8^5)# or

#z^z = 8^(-24/8^5)#

Now we have the format to use the Lambert #W# function to solve the equation.

https://en.wikipedia.org/wiki/Lambert_W_function

so with the help of https://www.wolframalpha.com/

#z=-(9log_e(2))/(2^12 W(-(9log_e(2))/2^12))=0.000176197#

after that we have

#y=2^13 z = 1.4434#