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

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Answer 1 · 2017-04-16T11:12:50

$y = 1.4434$

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.

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

after that we have

$y=2^13 z = 1.4434$

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