Possible termination of 3 lines

There is no mailing address listed for customer service, but customers can use the corporate mailing address for all correspondence.

AT&T Corporate
208 S. Akard St.
Dallas, TX 75202

If you had posted your question here we could have answered your question.

If I understand the blog, your problem is the $48.26 credit card charge?

According to the Edge agreement, you are required to pay state sales tax on the phone up front. Your state tax laws require it. The tax must be on the full retail price of the phone you purchased.
No other tax on the phone is collected on your AT&T bill.
http://www.att.com/shop/wireless/next.html

The first paragraph below address the tax: ( copied from the link)
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1AT&T NextSM: Requires 30-month, 24-month, or 20-month 0% APR installment agmt & well-qual. credit. Tax due at sale. For example, for a smartphone that has a full price of $825.99. It will be $27.54 a month for 30 months on AT&T Next 24, $34.42 a month for 24 months on AT&T Next 18, and $41.30 a month for 20 months on AT&T Next 12. Service: Wireless service (voice & data) req'd & is add'l. Device balance due if wireless svc cancelled. Select locations only. Device Limits: Purchase limit may apply. Account limit of four devices via AT&T Next or tablet installment agmt (total of 2 tablets) may also apply. Restocking Fee: up to $35. Upgrade Options: Req's payment of number of req'd installments (24, 18, or 12) based on option chosen (AT&T Next 24, 18, or 12), acct in good standing, trade-in of your financed device in good physical and fully functional condition, & purchase of new elig. device w/ qual. wireless svc. After upgrade, unbilled installments are waived. Service subject to Wireless Customer Agmt. Other fees may apply. Other Monthly Charges/Line: May include taxes & federal/state universal svc charges, Reg. Cost Recovery Charge (up to $1.25), gross receipts surcharge, Admin. Fee & other gov't assessments which are not gov't req'd charges. Coverage & svc not avail everywhere. Other restr's apply & may result in svc termination. Terms, restrictions and options subject to change and may be modified, terminated, or discontinued at any time without notice.

2 Mobile Share Value: Prices include a monthly plan charge and per-device monthly access charge. Devices: Sold separately. AT&T Next installment charges or other device purchase costs are extra. Discounted Access Charge: Access charges for smartphone lines on No Annual Service Contracts (AT&T Next, bring your own, pay full price, or month-to-month) are discounted up to $25 per month when compared to smartphone lines on new 2-year contracts. The discount will be $25 per smartphone line on plans 10GB and higher, and $15 for plans less than 10GB. For plans 10GB or higher, customers with smartphones on 2-year contracts prior to February 2, 2014, also are eligible for the $15 per month discounted access charge. For plans 2GB to 6GB, customers with smartphones on 2-year contracts prior to March 9, 2014, are also eligible for the $25 per month discounted access charge. This discount is available as long as you keep your phone. Upgrade: If upgrading to a new smartphone, the discounted access charge is only available via AT&T Next, when you bring your own smartphone, or if you buy a new smartphone at full price. If you upgrade to a new 2-year contract, the discount is lost for that line. Data: If you exceed the amount of data in your plan (including available Rollover DataSM) during your billing period, an additional 300MB, 500MB, or 1GB is automatically provided as specified in your rate plan. Unless otherwise specified, data allowances—including overages and Rollover Data—must be used in the billing period provided or they will be forfeited. Tethering and mobile hotspot use is allowed for up to 5 simultaneous devices. Rollover Data: Mobile Share Value plans only. Unused data from your monthly plan allowance rounds up to the nearest MB and carries over for one billing period. Unused Rollover Data automatically expires after one billing period or with any plan change (such as changing data amounts or termination). Unused overage data does not roll over. Rollover Data is always consumed last, after your other data allowances. Device Limits: 10 per plan for consumers and Individual Responsibility Users (IRUs). Limit 4 financed devices per wireless account may apply.

3 Smartphone 2-year contract pricing: Requires new 2-year wireless agreement with a qualified plan (voice and data). Equipment price may vary by market and location. Subject to Wireless Customer Agreement. Activation or upgrade fee up to $40 per line and additional deposits may apply. Credit approval is required. Geographic, usage, and other restrictions apply and may result in service termination. Coverage and services are not available everywhere. Sales tax and other charges apply. Data: If usage exceeds your monthly data allowance, you will automatically be charged overage for additional data provided. Early Termination Fee (att.com/equipmentETF): After 14 days, ETF up to $325. Restocking fee: up to $35. Pricing and terms are subject to change.
4 Purchases of smartphones via AT&T Next are not eligible for employee discounts. Employee discounts are for the wireless service only.

General Wireless Service Terms: Subject to Wireless Customer Agreement. Credit approval may apply. Activation or upgrade fee up to $40 per line and deposit may apply. A fee may be charged if you convert from a prepaid (GoPhone®) or session-based plan. Other Monthly Charges per Line: May include taxes, federal and state universal service charges, a Regulatory Cost Recovery Charge (up to $1.25), gross receipts surcharge, Administrative Fee, and other government assessments which are not government-required charges. Restrictions apply and may result in service termination. Pricing, terms, restrictions, and options are subject to change and may be modified, discontinued, or terminated at any time without notice. Coverage and service are not available everywhere.

It wouldn't have made a difference. It's a state requirement. No matter where you purchased you would have been required to pay sales tax. And all retailers are required to collect this money up front. The state wants their tax.
Your only way to avoid it is to (physically) buy a phone in one of the few states (like Wisconsin) that has no state sales tax.

You would have signed a credit charge slip for the tax. It should have been on your sales slip as amount tendered at sale. (That is how mine appears)

Just as a matter of security, why didn't you ask why your credit card was required?
(Don't make me haul out that old chestnut about the word "assume" making you know what out of U and Me) 😜
With the amount of paperwork involved, I can easily see one thing being forgotten. So despite you not being told, the subject should have come up when they asked for your card number. It's a mom thing, so I have to say, they didn't ask for nothing.

I think you agree the charge was valid. It's $48.46. So how much is making a point worth? Keep in mind, it will cost you something to switch carriers if that is your line in the sand.