this works:

 echo `date`
 echo `uptime`

but is better this way:

 echo $(date)
 echo $(uptime)

(read about why [here][1])


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And, in this particular case, you'll probably be fine just with:

 date
 uptime

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this:

 cat /home/rpeb/example.sh 1> /home/rpeb/example.log

**will not** execute your script.

`cat /home/rpeb/example.sh` is just printing the content of `/home/rpeb/example.sh`

and then, you are redirecting `stdout` from that command, to the file `/home/rpeb/example.log`. So, what your are really doing here, is making a copy of `/home/rpeb/example.sh` into `/home/rpeb/example.log`.
Seems that this is not what you want.

But in case you do, this is more succinct:

 cat /home/rpeb/example.sh > /home/rpeb/example.log

when you just use `>`, the `1` before it is implied.


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If you want to run the script `/home/rpeb/example.sh`, and then redirect its output to the file `/home/rpeb/example.log`, first, give execute permissions to `/home/rpeb/example.sh`, this way:

 chmod u+x /home/rpeb/example.sh

then, you run the script, simply writing its path, then redirecting its output, like this:

 /home/rpeb/example.sh > /home/rpeb/example.log

and, btw, if both files (your script, and your log to be) are in the same `dir`, and you are inside that `dir`, you con simply run:

 ./example.sh > example.log

And if you want the output from `example.sh` printed on your terminal, and logged into `example.log`, you can do that this way:

 ./example.sh | tee example.log

 [1]: http://mywiki.wooledge.org/BashFAQ/082