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printf() ---> printf() in the C library ---> write() in C library ---> write() system call in kernel.

Following the trail from printf down to the actual OS call(s) can be pretty messy.To understand what is going on at the lowest levels, you will need to analyze the source code in the kernel.

For ques printf
Printf function calls the write function in the kernel

I wonder if the question is just how printf takes a format string, a list of args, constructs a string from it and then writes it to console. I atleast would like to know the answer to this though.

printf() call will lead to calling the write() function which thus writes the data to the output stream,stdout.

printf() is implemented in libc (standard library) which use the "write" system call to out the string in stdout or stderr. Inside libc, printf implementation takes variable arguments, and formats the strings using format specifier "%" and finally output the string to stdout or stderr using "Write" system call.

Using the C header file cstdarg which allows you to define variable parameter functions.

Using code, with a keyboard. TADA....!