Not-so-hard logarithm equation

You can easily solve this using the definition of logarithm that is:

$\large log _{ a }{ b } =\quad c$

Then:

$\large { a }^{ c }=\quad b$

Using this at the problem this happens:

$\large log _{ 11 }{ (\log _{ 5 }{ x)\quad = } { 2 }^{ -1 } }$

$\large { 2 }^{ -1\quad }=\quad \frac { 1 }{ 2 }$

Then:

$\large log _{ 5 }{ x\quad =\quad } { 11 }^{ \frac { 1 }{ 2 } }$

$\large { 11 }^{ \frac { 1 }{ 2 } }=\quad \sqrt { 11 }$

Implies that:

$\large log _{ 5 }{ x } =\quad \sqrt { 11 }$

And, to finish:

$\large x\quad = \quad { 5 }^{ \sqrt { 11 } }$

Thanks !