is <math.h> for C or C++?

Im needing the natural logarithm function for use in a .cpp (c++) source file. Now, of course I can do this with a quick google search and a simple library solution. But Im a bit confused...

On the cplusplus dot com website under reference/cmath/log/ they have an example of how to use the log function, as follows

/* log example */
#include <stdio.h>      /* printf */
#include <math.h>       /* log */

int main ()
{
   double param, result;
   param = 5.5;
   result = log (param);
   printf ("log(%f) = %fn", param, result );
   return 0;
}

some questions i have:

1) Why are they using

<stdio.h>

I thought this was for C and not really for C++ ?

2) Why are they using

<math.h>

I though the .h represented C header files rather than the .hpp C++ header files?

Forgetting about the use of stdio (i'll use iostream anyway) but even so by using

<math.h>

It feels like I'm writing C code and not C++ code. Im learning C++ through a taught course and the instructor covered C in the first week and then said we wont be using C again but will be using C++ from now on. I feel like I wont be able to explain myself if the teacher asks "why did you use a C header file? You are supposed to be working in C++".

Any explanations much appreciated.