CAT Exam Model Paper 4 with solutions for free online practice

${\left(\mathit{x}-7\right)}^{\left(\frac{{\mathit{x}}^2-29\mathit{x}+154}{{\mathit{x}}^2-12\mathit{x}+32}\right)}=1$
⇒ ${\left(\mathit{x}-7\right)}^{\frac{\left(\mathit{x}-7\right)\left(\mathit{x}-22\right)}{\left(\mathit{x}-8\right)\left(\mathit{x}-4\right)}}=1$
Let P(x) = (x - 7) and Q(x) $=\frac{\left(\mathit{x}-7\right)\left(\mathit{x}-22\right)}{\left(\mathit{x}-8\right)\left(\mathit{x}-4\right)}$
Now, three cases arise:
Case-1P(x) = 1 and Q(x) may be anything.
∴(x-7) = 1
or x = 8
But, for x = 8, Q(x) is not defined.
Case-2
P(x) = - 1 and Q(x) is an even exponent.
(x - 7) = - 1 or x = 6
For x = 6, Q(x) = - 4, which satisfies the given equation.
Case -3Q(x) = 0 and P(x) ≠ 0
∴$\frac{\left(\mathit{x}-7\right)\left(\mathit{x}-22\right)}{\left(\mathit{x}-8\right)\left(\mathit{x}-4\right)}=0$
⇒ x = 7 or x = 22
But, for x = 7, P(x) = 0, for which the given equation is not defined.
So the given equation is satisfied for two values of ‘x' (6 and 22).