MathDB

Math Prize 2010 Problem 17

Source:

November 14, 2010

functionlogarithms

Problem Statement

For every

x \ge -\frac{1}{e}\,

, there is a unique number

W(x) \ge -1

such that

W(x) e^{W(x)} = x.

The function

W

is called Lambert's

W

function. Let

y

be the unique positive number such that

\frac{y}{\log_{2} y} = - \frac{3}{5} \, .

The value of

y

is of the form

e^{-W(z \ln 2)}

for some rational number

z

. What is the value of

z

?

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