How to stop My iPhone 4 power off problem?

IIm using iPhone 4. From few days ago my phone shutting down repeatedly when I want to make a call or text to anyone and an apple logo stuck on the screen. When I use Wi-Fi and other services phone remain switch on and interestingly while phone is connected to the charger I can make a call or text.
What can I do now?

Take it back to where you got it. If that's not possible… Take it to your carrier's store.

Sounds like a bad battery.

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