Find root of the equation Find maximum root of the equation $$x - \frac{1000}{\log 2} \log x = 0$$
It locates between $13746$ and $13747$, but I want to find right solution not using graphing calculators. Thanks in advance.

$$x-\frac{1000\ln(x)}{\ln(2)}=0\Longleftrightarrow$$
$$-\frac{1000\ln(x)}{\ln(2)}=-x\Longleftrightarrow$$
$$\frac{1000\ln(x)}{\ln(2)}=x\Longleftrightarrow$$
$$1000\ln(x)=x\ln(2)\Longleftrightarrow$$
$$e^{1000\ln(x)}=e^{\ln(2)x}\Longleftrightarrow$$
$$x^{1000}=2^x\Longleftrightarrow$$
$$x=\exp\left[-\text{W}\left(-\frac{\ln(2)}{1000}\right)\right]\approx13746.809166647028809$$
