Question 803391
I see no mistake in b), and it seems to be the most direct way to the answer.
 
In a), I believe that the problem is that
{{{ 3 ^ x = log( 2, ( log( 2, 2 ^ 8 ) ) ) }}} means that
{{{ 2 ^ ((3 ^ x ))= log( 2, 2 ^ 8 ) }}}
I see those parentheses around {{{3^x}}} as crucial to establish the proper meaning of the expression.
 
Certainly, {{{ 2 ^ ((3 ^ x ))}}} is not the same as {{{( 2 ^ 3 )^ x = 2^(6x)}}} as you assumed to keep on going.
If {{{x=5}}}, {{{ 2 ^ ((3 ^ x ))= 2 ^ ((3 ^5))=2^243}}},
while {{{( 2 ^ 3 )^ x = ( 2 ^ 3 )^ 5=8^5=2^15}}}
 
Probably there are rules about order of operations that assign one or another meaning to {{{2^3^x}}}, but I would forget them soon after reading them, because those expressions do not come up too often, so I will use parentheses to make my meaning clear.
 
In any case, I would not know how to proceed further after getting to {{{ 2 ^ ((3 ^ x ))}}} , because I do not know of any equivalent expression.