A new definition of a multivalued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This new logarithm arises naturally from the definition of the cylinder transformation that is also the wellspring of the definition of exponential functions on time scales. This definition will lead to a logarithm function on arbitrary time scales with familiar and useful properties that previous definitions in the literature lacked.

中文翻译：

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时间尺度上的多值对数

引入了时间尺度上的多值对数的新定义，用于永不消失的增量可微分函数。这个新的对数自然来自于圆柱体变换的定义，这也是时间尺度上指数函数定义的源泉。该定义将导致任意时间尺度上的对数函数，具有先前文献中所缺乏的熟悉和有用的属性。