I think the OP has a pretty good case for this being an unauthorized charge.

Additionally, as someone who has been on the receiving end of chargebacks a number of times I can tell you merchants have a higher burden of proof in things like this. Even submitting perfect evidence can get ruled in favor of the cardholder.

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fckgw a day ago | parent [-]

Wouldn't the merchant's proof be the two emails they sent regarding the upcoming renewal with charges listed?

	▲	joshstrange a day ago \| parent \| next [-]
		Perhaps? Chargebacks are a completely black box though and the entity that makes the decision is the cardholder's issuer so they often rule in favor of the cardholder if there is even a chance they are right (in my experience). I've had what I thought was bullet-proof evidence before and lost an appeal (as a merchant).
	▲	anigbrowl a day ago \| parent \| prev [-]
		If they sent an email saying or clearly implying it would renew at $38 and the following 2 emails didn't have any clear warning about price changes in the subject line, I think OP would be quite justified in having assumed they were just empty reminders.