Question

Solve: ${\log }_4{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)=0$

Answer 1

Given:${\log }_4{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)$

${\log }_4{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)=0$

$4^{{\log }_4{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)}=4^0$

${\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)=1$

$2^{{\log }_2{\log }_{\sqrt{2}}{\log }_3(x-2006)}=2^1$

${\log }_{\sqrt{2}}{\log }_3(x-2006)=2$

${\sqrt{2}}^{{\log }_{\sqrt{2}}{\log }_3(x-2006)}={\sqrt{2}}^2$

${\log }_3(x-2006)=2$

$3^{{\log }_3(x-2006)}=3^2$

$\Rightarrow x-2006=9$

$\Rightarrow x=2015$