$L=2\log_{r}\left(\frac{\ln(\ln(x))+\ln(2)-\ln(\ln(5))}{\ln(2)}\right)$
$x>\sqrt{5}\text{ and }r\neq 1\text{ and }r>0$

$\left\{\begin{matrix}r=\left(\frac{\ln(\ln(x))+\ln(2)-\ln(\ln(5))}{\ln(2)}\right)^{\frac{2}{L}}\text{, }&x>\sqrt{5}\text{ and }L\neq 0\text{ and }\left(|\frac{\ln(\ln(x))-\ln(\ln(5))}{\ln(2)}+1|\right)^{\frac{1}{L}}\neq 1\text{ and }x\neq 5\\r\in \left(0,1\right)\cup \left(1,\infty\right)\text{, }&L=0\text{ and }x=5\end{matrix}\right.$