\(\displaystyle{\log{{16}}}{\left({x}\right)}={\left(\frac{{1}}{{4}}\right)}{\log{{2}}}{\left({x}\right)}\)

\(\displaystyle{\log{{4}}}{\left({x}\right)}={\left(\frac{{1}}{{2}}\right)}{\log{{2}}}{\left({x}\right)}\)

so you hav \(\displaystyle{\left({1}+\frac{{1}}{{2}}+\frac{{1}}{{4}}\right)}{\log{{2}}}{\left({x}\right)}={7}\)

\(\displaystyle{1.75}\cdot{\log{{2}}}{\left({x}\right)}={7}\)

\(\displaystyle{\log{{2}}}{\left({x}\right)}=\frac{{7}}{{1.75}}={4}\)

\(\displaystyle{x}={2}^{{4}}={16}\)

\(\displaystyle{\log{{4}}}{\left({x}\right)}={\left(\frac{{1}}{{2}}\right)}{\log{{2}}}{\left({x}\right)}\)

so you hav \(\displaystyle{\left({1}+\frac{{1}}{{2}}+\frac{{1}}{{4}}\right)}{\log{{2}}}{\left({x}\right)}={7}\)

\(\displaystyle{1.75}\cdot{\log{{2}}}{\left({x}\right)}={7}\)

\(\displaystyle{\log{{2}}}{\left({x}\right)}=\frac{{7}}{{1.75}}={4}\)

\(\displaystyle{x}={2}^{{4}}={16}\)