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Permutation: n Different Things Taken r at a Time

If 2 x-3 . ...

Question

If $2^{x - 3} . 3^{2 x - 8} = 36$ , then value of $x$ is ____ .

2

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3

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Solution

The correct option is A $5$
$2^{x - 3} \times 3^{2 x - 8} = 4 \times 9$
$2^{x - 3} \times 3^{2 x - 8} = 2^{2} \times 3^{2}$
$2^{x - 5} \times 3^{2 x - 10} = 1$
$x = 5$
as RHS is 1, the powers have to be zero on the LHS as anything raise to $0$ is always $1$
Thus $x - 5 = 0 \to x = 5$

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