[tex]110\cdot 10^{4x}=55\implies 10^{4x}=\cfrac{55}{110}\implies 10^{4x}=\cfrac{1}{2}\implies 10^{4x}=2^{-1} \\\\\\ \log\left( 10^{4x} \right)=\log\left( 2^{-1} \right)\implies 4x\log_{10}\left( 10 \right)=-1\log_{10}(2)\implies 4x(1)=-\log(2) \\\\\\ 4x=-\log(2)\implies x=-\cfrac{\log(2)}{4}\implies {\LARGE \begin{array}{llll} x\approx -0.08 \end{array}}[/tex]
