Question:
Mark (✓) against the correct answer
If $\left(\frac{5}{12}\right)^{-4} \times\left(\frac{5}{12}\right)^{3 x}=\left(\frac{5}{12}\right)^{5}$, then $x=?$
(a) $-1$
(b) 1
(c) 2
(d) 3
Solution:
(d) 3
$\left(\frac{5}{12}\right)^{-4} \times\left(\frac{5}{12}\right)^{3 x}=\left(\frac{5}{12}\right)^{5}$
$\Rightarrow\left(\frac{5}{12}\right)^{-4+3 x}=\left(\frac{5}{12}\right)^{5}$
$\Rightarrow-4+3 x=5$
$\Rightarrow 3 x=5+4=9$
$\Rightarrow x=\frac{9}{3}=3$
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