Best way to add a "prompt" message to std::cout

Best way to add a "prompt" message to std::cout

I'm searching the best way to add a custom, initial message to all the
messages that std::cout (or std::cerr) prints to console/file output.
For example, if I setup that this custom prompt message will be the string
"[Log]", then a classic
std::cerr << "This is a log message" << std::endl;
will be printed in this way:
> [Log] This is a log message
Clearly I can obtain this behavior using
std::string PROMPT_MSG = "[Log]";
std::cerr << PROMPT_MSG << "This is a log message" << std::endl;
but I'd like a less invasive way.
Thanks in advance