Question about Super Saiyan Multipliers

I recently learned that the only official multiplier accepted in dragon ball is the Kaioken multiplier(because it's officially stated to multiply strength speed and agility which is absolutely true, no argument). Although the super saiyan transformation multipliers aren't accepted because they multiply power levels (which are non-linear). Although in the saiyan saga Goku is confirmed to have a power level of 8000(maybe 9000) and Vegeta has a power level of 18000. Goku using kaoiken x 2 allowed him to fight on par with Vegeta which means that he also DOUBLED his power level. Which shouldn't be the case if power levels are non-linear. Super Saiyan is stated to be a 50x increase of power level by official guidebooks, and if we use our reasoning from the kaoiken multiplier we can take the super saiyan transformation as a 50x increase to all of a person's stats.

Also just to refute an argument on the spot.

When characters use attacks like Kamehameha, their power level often increases dramatically, which is why goku had to increase his kaoiken multipler when in his beam struggle against saiyan saga vegeta.

So, in conclusion, should we accept the super saiyan multipliers or not? Because the whole power level being non-linear is very inconsistent and for simplicities sake should be ignored when not reasonable(at least in context).

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I don't know. Im aware when he uses kasioken he multiplies his power just like the ssj forms but im sure there's other reasons outside of massively inflated results if the ssj multipliers are put in place, which would also lead to all power scaling multipliers to be accepted than he got shit like solar system frieza, mftl saiyan saga, bullshit mftl cell and buu and outliers are everywhere. Of course i like dbz but i can see where this could lead unless explicitly stated in story.

Actually, the first time goku exceeded light speed was in the namek saga when he went super saiyan. He crossed half of namek instantly or something, which made him like 1/14 speed of light, stacking on ss multiplier made him 50/14 speed of light or something like that. Don't quote me on this, although I do know that this would explain why a 5 minute fight on namek took 100 episodes.

No.

Power level ain't linear. The only times where it is linear is when Kaioken is involved, otherwise it ain't.

Look at the difference between 23rd Budoukai Goku and Raditz, in both power level and actual strength. Or between Vegeta and Freeza. Or between an ordinary human and Kid Goku.

Power levels accomplish no purpose other than to determine who is stronger than who. We obviously cannot use them for linear scaling purposes.

The Super Saiyan Multipliers are:

• Power level based (x50 comes from the stated Power levels for Base Goku and SSJ Goku)
• Never stated in the show proper
• Contradicted by the actual show (See Gohan vs Cell)

Also Goku didn't cross half of Namek, that is contradicted by the actual manga. The ships were very close. And we cannot use Super Saiyan Multipliers for Goku's speed.