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要使函數的解析有有意義則2x+1>0故函數的定義域為(-12,+∞)由於內函數u=2x+1為增函數,外函數y=log5u也為增函數故函數f(x)=log5(2x+1)在區間(-12,+∞)單調遞增故函數f(x)=log5(2x+1)的單調增區間是(-12,+∞)故答案為:(-12,+∞)
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