If 2^{x-2} cdot 3^{2x-6} = 36,then find x. | vedclass

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(C) Given equation: $2^{x-2} \cdot 3^{2x-6} = 36$We know that $36 = 6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2$.So,the equation becomes: $2^{x-2} \cdot 3^{2x

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$4$

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(C) Given equation: $2^{x-2} \cdot 3^{2x-6} = 36$We know that $36 = 6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2$.So,the equation becomes: $2^{x-2} \cdot 3^{2x-6} = 2^2 \cdot 3^2$.By comparing the powers of $2$ and $3$ on both sides:For base $2$: $x - 2 = 2 \implies x = 4$.For base $3$: $2x - 6 = 2 \implies 2x = 8 \implies x = 4$.Since both conditions yield $x = 4$,the value of $x$ is $4$.

If $2^{x-2} \cdot 3^{2x-6} = 36$,then find $x$.

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