The range of log5⁡[2(sin⁡x−cos⁡x)+3] is

f(x)=2 sinx-2cosx+3 Range=3-2+2, 3+2+2=1,5 The range of log5⁡[2(sin⁡x−cos⁡x)+3] is log51,log55=0,2

The range of log5⁡[2(sin⁡x−cos⁡x)+3] is

f(x)=2 sinx-2cosx+3 Range=3-2+2, 3+2+2=1,5 The range of log5⁡[2(sin⁡x−cos⁡x)+3] is log51,log55=0,2

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

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$[1, 2]$

$[1, 3]$

$[0, 2]$

$[0, 3]$

answer is A.

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$f (x) = \sqrt{2} \sin x - \sqrt{2} \cos x + 3 R a n g e = 3 - \sqrt{2 + 2}, 3 + \sqrt{2 + 2} = 1, 5 The range of \log_{\sqrt{5}} [\sqrt{2} (\sin x - \cos x) + 3] is [\log_{\sqrt{5}} 1, \log_{\sqrt{5}} 5] = [0, 2]$

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The range of log5⁡[2(sin⁡x−cos⁡x)+3] is

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