Question 113802
<pre><font size = 4><b>
{{{ log(8,(log(4,(log(2,x) ) ))) }}}={{{0}}}
    
Using the rule {{{b^log(b,A)}}} = {{{A}}},
raise 8 to the left side power and set
that equal to 8 raised to the right
side power:

{{{ log(8,(log(4,(log(2,x) ) ))) }}}={{{0}}} 

{{{8^ log(8,(log(4,(log(2,x) ) ))) }}} = {{{8^0}}}

Simplify using the rule above

{{{log(4,(log(2,x)  )) }}} = {{{1}}}

Remembering that same rule again,
raise 4 to the left side power and set
that equal to 4 raised to the right
side power: 

{{{4^log(4,(log(2,x)  )) }}} = {{{4^1}}}
  
Using that rule, raise 4 to the left side 
power and set that equal to 4 raised to 
the right side power: 

Simplify using the same rule:

{{{log(2,x)   }}} = {{{4}}}

Remembering that same rule one final time,
raise 2 to the left side power and set
that equal to 2 raised to the right
side power:

{{{2^log(2,x)   }}} = {{{2^4}}}

Simplify using the same rule:

{{{x}}} = {{{16}}}

Edwin</pre>