Hi,
Every exchange adding a new btc, eth, token address on the exchange website.
I think they need some private key to set the transaction on this websites.
So is this private key stored in a normal database?
And is this safe?
Exchanges are safe enough for you to carry out your trading activities but not safe enough for you to use them as a wallet to store your coins. You are more at risk of losing your coins if you leave them in an exchange than if you have them in your own personal wallet. The fact is that if you do not control the private keys to the wallet then you do not control your coins.