Solving non linear equation for x

Solving non linear equation for x

x^2 ln(0.4956/x) = (1-x)^2 ln(0.47198/(1-x)

Can somebody solve this equation for me?

I'm finding little difficulty in this

Answer 1

[Alan Weiss]

eqn = @(x) x.^2 .* log(0.4956./x) - (1-x).^2 .* log(0.47198./(1-x));
t = linspace(0.01,0.99);
plot(t,eqn(t)) % Shows a single real root in this interval

x = fzero(eqn,[0.01 0.99])

x =

0.5115

No toolboxes needed.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[madhan ravi]

syms x
x=vpasolve((x.^2.*log(0.4956./x) == (1-x).^2.*log(0.47198./(1-x))))

Gives:

x =
0.52091005935042057378274263984089 - 1.0079858568869724875750086505265i
>> 

Answer 3

[Star Strider]

Using the Optimization Toolbox fsolve function:

eqn = @(x) x.^2 .* log(0.4956./x) - (1-x).^2 .* log(0.47198./(1-x));
xval = fsolve(eqn, 10)

produces:

xval =
           0.51145093065171 +  9.06147769514677e-09i