We know that the ship has and creates logs, even the captains and various crew members will write personal logs.

Why then, do they rely on logs when it can be manipulated? I'm sure a determined engineer can manipulate the logs to make an explosion look "unplanned".

The only I can see the logs being reliable is if there is some form of version control and backup. So you make a log and check it into the system, at which point, it creates a copy that no one, not even the captain can manipulate. If you want to make any changes, you are given a copy to do so, and when you check your changes in, it's also copied to a secure location.

Higher ranking members can access the logs and view all the changes that were made.

Federation (and other) logs are, for the most part, susceptible to manipulation by computer experts. The principle is that if they're used as the basis for legal proceedings that they're treated as any other piece of evidence, normally highly reliable but potentially alterable.

GRAL: These accusations are absurd. We had nothing to do with this alleged attack.

ARCHER: The Andorian sensor logs. Look them over yourself.

GRAL: Logs can be fabricated.

_{^{ENT: Babel One}}

and

DAX: If you want, you can check our ship's logs and they'll prove it to you.

COLYUS: Logs can be tampered with. Well, you ought know that. After all, you claim to be a Security Officer.

_{^{DS9: Shadowplay}}

Note that there are ways of cross-checking the logs with other logs to confirm their veracity

DATA: By comparing the Stargazer's main computer log with Captain Picard's personal log, I have found checksum discrepancies, sir.

RIKER: What does that mean?

DATA: All information is time-coded by entry, and the bits when totaled produce an aggregate amount which

_{^{TNG: The Battle}}

And later in DS9 we see that there are some kinds of logs (highly specialised, rarely used, extraordinarily expensive) that are basically unfakeable.

GARAK: When Senator Vreenak arrives, you will show him a holographic recording of a secret meeting held at the highest level of the Dominion in which the planned invasion of Romulus is being discussed. You will tell the Senator that this information was obtained through various covert means at great cost to the Federation. At least ten good men lost their lives bringing it across the line, that sort of thing. He will immediately suspect it's a forgery, but you will assure him that such a thing would be impossible. You see, Senator, this is an official Cardassian transcript. It was recorded on a one time optolythic data rod used for official record keeping. These rods are manufactured only as needed on Cardassia Prime. Information can only be transcribed on them once, and then cannot be altered.

SISKO: He'll want to examine it.

_{^{DS9: In the Pale Moonlight}}

Interestingly, the log in TOS: Court Martial is recognised as being susceptible to tampering but since the only ones who could tamper with it are Kirk (the accused), Spock (his loyal Number One and basically above suspicion) and the victim, the idea that it might be inaccurate was discounted out of hand until Spock noticed that the computer was acting funny.

COGLEY: Hypothetically, Mister Spock. Hypothetically, Miss Shaw. If what you suggest had been done, it would be beyond the capabilities
of most men. Is that true?

SPOCK: Affirmative.

COGLEY: What man aboard ship would it not be beyond?

SPOCK: The Captain, myself, and the records officer.

_{^{TOS: Court Martial}}

The chain of command can benefit from inaccurate logs.

According to Captain Janeway, Starfleet captains, in the best interest of carrying out their responsibilities, sometimes require greater freedom to act than Federation law and Starfleet regulations can officially sanction. Call this the idealistic explanation:

JANEWAY: It would seem that Captain Sulu decided not to enter that journey into his official log. The day's entry makes some cryptic remark about the ship being damaged in a gaseous anomaly and needing repairs, but nothing else.

KIM: You mean he falsified his logs?

JANEWAY: It was a very different time, Mister Kim. Captain Sulu, Captain Kirk, Dr. McCoy. They all belonged to a different breed of Starfleet officer. Imagine the era they lived in. The Alpha Quadrant still largely unexplored. Humanity on verge of war with Klingons. Romulans hiding behind every nebula. Even the technology we take for granted was still in its early stages. No plasma weapons, no multiphasic shields. Their ships were half as fast.

^{— "Flashback" (Voyager, 3x02)}

There is also a self-serving interpretation. Captain Sulu's inaccurate log, in this instance, omitted the fact that his illegal order resulted in the death of at least one crew member under his command. It's unknown how Starfleet dealt with this breach of regulations and ethics, although Sulu's career and reputation does not seem to have suffered for it.

"Court Martial" (TOS, 1x14) established that ships' computers keep audio-video records of the bridge. In addition to putting a favourable spin on his own log, Captain Sulu would have needed to alter the bridge recording to keep the events out of Starfleet's official record.