The number of solutions of ${log}_{3} (x - 3) = 4 - x$ is

0

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1

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2

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infinite

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Solution

The correct option is B $1$
$x - 3 = 3^{4 - x}$
Let $y = x - 3$
$\Rightarrow y = 3^{4} \cdot 3^{- x}$

Clearly, from the graph, we can say only one solution exists.

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