Solution(s) of the equation x^ ( _ 10 x+7 4 ) =10^ _ 10 x+1 , is/are

$x^{\left(\frac{\log _{10} x+7}{4}\right)}=10^{\log _{10} x+1}$ Taking log both sides on base, we get \left(\frac{\log _{10} x+7}{4}\right) \log _{10} x=\left(\log _{10} x+1\right) \log _{10} 10$Put,$\log _{10} x=1\therefore(t+7) t=4 t+4\Rightarrow t=-4,1x=10^{-1}, 10