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The range of $\log_{\sqrt{5}} [\sqrt{2} (\sin x - \cos x) + 3]$ is

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[0, 3]

[0, 2]

[1, 2]

[1, 3]

answer is B.

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Detailed Solution

Range = $2 \log_{5} [1, 5] = [0, 2]$

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