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Logarithmic diminishing marginal value is a version of diminishing marginal value that specifically *doesn't* have a bounded positive contribution for each term.

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this has nothing to do with logarithmic diminishing marginal value. they were just applying a log to both sides to demonstrate that the utility function can be monotonically transformed to an additive function with a constant slope (with the implicit assumption of ordinal utility theory)

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Conceptually, you are right, but formally, this is identical to logarithmic diminishing marginal value.

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