FCL.050 Recording of flight time
The pilot shall keep a reliable record of the details of all flights flown in a form and manner established by the competent authority.
AMC1 FCL.050 is more specific in how this should be done. The conclusion is: Yes, you may use an electronic log in an EASA compliant format, however, it only becomes an official document when printed and signed!
FCL.045 Obligation to carry and present documents
(a) A valid licence and a valid medical certificate shall always be carried by the pilot when exercising the privileges of the licence.
(b) The pilot shall also carry a personal identification document containing his/her photo.
(
c) A pilot or a student pilot shall without undue delay present his/her flight time record for inspection upon request by an authorised representative of a competent authority.
I can assure you that the inspectors interpretation of "without undue delay" means before he's leaving the aircraft!
It is advisable to carry a print out with you (i.e to proof recency!).
@mushroom 69: I don't know about other countries, but on Swiss licences only hand entries of Swiss examiners and only for the purpose of revalidation are accepted!
Cheers,
g5tom