Solve for x. x^2 = 2^x Do I take the natural log on both sides as step 1?
x^2 = 2^x prepare for Lambert form xe^(-(ln(2)x)/2)=1 rewrite the equation with -(ln(2)x)/2)=u and x=-(2u)/ln(2) -(2u)/ln(2)*e^u=1 rewrite -(2u)/ln(2)*e^u=1 in Lambert form (e^u)u=-ln(2)/2 solve e^u=-ln(2)/2=> u=-2ln(2), u=-1*ln(2) substitute back u=-(ln(2)x)/2), solve for x -2ln(2)=-(ln(2)x)/2 -4ln(2)=-ln(2)x -4=-x x=4 -1*ln(2)=-(ln(2)x)/2 -2*ln(2)=-ln(2)x -2=-x x=2
Lambert's function, also called the "W" function (Lambert W-Function -- from Wolfram MathWorld) is defined as the inverse function to f(x)= xe^x.
Did you try looking for him yourself? Johann Heinrich Lambert (1728 - 1777) - Biography - MacTutor History of Mathematics (st-andrews.ac.uk)