Solve for $r : 27^{6 - r} = 9^{r - 1}$

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Solution

The correct option is D 4
Given, $27^{(6 - r)} = 9^{(r - 1)}$ $\Rightarrow 3^{3 (6 - r)} = 3^{2 (r - 1)}$
By comparing powers, we get
$18 - 3 r = 2 r - 2$
$\Rightarrow 5 r = 20$
$\Rightarrow r = \frac{20}{5} = 4$

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