The Lambert W function, also known as the omega function, is a special function that is defined as the inverse of f(x)=xe^x. In other words, for a given value of y, the Lambert W function returns the value of x that satisfies the equation y=xe^x.
The Lambert W function is commonly used to solve equations that involve both a variable and an exponent. It allows for the variable to be isolated on one side of the equation, making it easier to solve.
This equation is a type of exponential equation, where both sides contain variables raised to an exponent. It involves finding the value of x that satisfies the equation when x is equal to a power of 2.
The equation can be rewritten as x^2=e^(xln2). By taking the natural logarithm of both sides, we can isolate the variable and apply the Lambert W function to solve for x. The solution is x=-2W(-ln2).
There are two possible solutions for this equation, which are x=2 and x=-2W(-ln2). However, the solution x=2 does not satisfy the original equation, so the only valid solution is x=-2W(-ln2).