If it outputs to stderr as well you’ll want to silence that. You can do that by redirecting file descriptor 2:
# Send stdout to out.log, stderr to err.log
myprogram > out.log 2> err.log
# Send both stdout and stderr to out.log
myprogram &> out.log # New bash syntax
myprogram > out.log 2>&1 # Older sh syntax
# Log output, hide errors.
myprogram > out.log 2> /dev/null