How to solve a logarithmic equation?

I need to solve the equation 7X*log(X)-2=0 in matlab where 0<X<1. How such equations are solved through MATLAB? I have used fsolve single variable and there was no answer with an error message of: Optimization running. Objective function value: 0.0 Zero find terminated.

Answer 1

[Torsten]

X = exp(lambertw(2/7))

Plot the function and you will see that there is no root for 0<X<1.

Best wishes

Torsten.

[Hanif Malekpoor]

Actually there is a root for this function near 0.64

[Torsten]

No.

http://www.wolframalpha.com/input/?i=f(x)%3D7*x*log(x)-2

Best wishes

Torsten.

[Jan]

There is a root for @(x) real(7*X*log(X)-2) at -0.6398364478 and one at 1.255537045

Answer 2

[Jan]

No, no root here:

x = linspace(0,1,1000);
plot(x, 7 * x .* log(x) - 2);

Of course this is not a proof. But you can show easily, that 7*x*log(x) is smaller than 0 inside [0,1] such that subtracting 2 can never lead to a 0.