Mathematic Problems
${x}^{\frac{{\mathrm{log}}_{10}\left(x+5\right)}{3}}={10}^{5+{\mathrm{log}}_{10}\left(x\right)}\phantom{\rule{0ex}{0ex}}$
${x}^{\frac{{\mathrm{log}}_{10}x+5}{3}}=\frac{{10}^{5+{\mathrm{log}}_{10}x}}{{l}{o}{{g}}_{10}{10}}$
${x}^{\frac{1}{3}\left({\mathrm{log}}_{10}x+5\right)}=\frac{{10}^{5+{\mathrm{log}}_{10}x}}{{1}}$
${l}{o}{{g}}_{10}{x}^{\frac{1}{3}{·}\left({\mathrm{log}}_{10}x+5\right)}={l}{o}{{g}}_{10}{10}^{{5}{+}{l}{o}{{g}}_{10}{x}}$
$\frac{1}{3}{·}\left({\mathrm{log}}_{10}x+5\right)·{l}{o}{{g}}_{10}{x}=\left(5+lo{g}_{10}x\right)·{l}{o}{{g}}_{10}{10}$
$\frac{1}{3}·\left({\mathrm{log}}_{10}x+5\right)·{\mathrm{log}}_{10}x=\left(5+{\mathrm{log}}_{10}x\right)·1$
${\mathrm{log}}_{10}x=t$
$\frac{1}{3}·\left(t+5\right)·t=5+t$
${t}_{1,2}=\frac{-2±\sqrt{{2}^{2}-4·1·\left(-15\right)}}{2}$
${t}_{1,2}=\frac{-2±\sqrt{4+60}}{2}=\frac{-2±\sqrt{64}}{2}$
${t}_{1,2}=\frac{-2±8}{2}$
${t}_{1,2}=-1±4$
${\mathrm{log}}_{10}{x}_{1}=3$
${x}_{1}={10}^{3}=1000$
${\mathrm{log}}_{10}{x}_{2}=-5$
${x}_{2}={10}^{-5}=\frac{1}{{10}^{5}}$
$x\in \left\{{10}^{3},{10}^{-5}\right\}$
$x\in \left\{{10}^{3},{10}^{-5}\right\}$