Question

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Eqn =======> Equation

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Answer 1

Hey

$\frac{ log_{12}( log_{8}( log_{4}(x) ) ) }{ log_{5}( log_{4}( log_{y}( log_{2}(x) ) ) ) } = 0$

When the expression is defined :

$log_{12}( log_{8}( log_{4}(x) ) = 0$
and

$log_{5}( log_{4}( log_{y}( log_{2}(x) ) ) ) \neq0$

From first Equation :

$x = {2}^{16}$
$y \neq 2$
However, the ridiculous part is :

$y \neq (0) \: or \: (1) \: or \: {z}^{ - }$

Okay, for this we jump in on the Theory part !!

Clearly this inequality must not hold :

$log_{4}( log_{y}(16) ) \leqslant 0$

And hence, 'y' never satisfies the inequality :

$y \geqslant 16$

Again, Intuitively, one can also state that :

$y > 1$
Hence, we arrive at a general pair of soln.

$1 < y < 16$
where

$y \neq 2$
And hence,

$a = 2$
$c = 1$
$b= 16$

And so,

$(a + b + c) = 19$

Answer 2

a+b= 19

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