Modifying interval modifier again and again

I read anki manual on changing interval modifier. I am creating a new deck and want low retention of 60% - so out of experience I would want to start with an interval modifier of 130% ( just a gut call).
Let us assume after 30 days I find my retention to be 75% and hence need to increase my interval modifier again.
So as per manual it will be log(60%)/log(75%) = 1.77 - Now should my new interval be 177% or 177*130%

I am asking this because I started with a base of 130% instead of 100%.Will the formula take care of the base change or I have to multiply it with the 130%? Could you please explain the science behind this briefly if possible - just for an intuitive idea?

Thanks a lot in advance

Relevant parts of manual:

On the SuperMemo website, they suggest that you can find an appropriate multiplier for a desired retention rate. Their formula boils down to:
log(desired retention%) / log(current retention%)

Imagine we have a current retention rate of 85% and we want to increase it to 90%. We’d calculate the modifier as:

log(90%) / log(85%) = 0.65

If you plug the resulting 65% into the interval modifier, you should find over time that your retention moves closer to your desired retention.

I googled around and on
found something relevant:

An equation for Ebbinghaus’s forgetting curve (see Forgetting Curve at Wikipedia) can be used to calculate the following equation found in the Anki manual:

New Modifier = Current Modifier * log(desired success ratio) / log(current success ratio)

However that blog cited Wikipedia but I couldn’t confirm that formula on either Wikipedia or any other website- morever Wikipedia is not a very reliable source

Please confirm this is true and if it is - I am sorry to take up your time. This was important for me as a medical student using anki extensively - this setting matters and the potential for screw up is huge.

Could I request to confirm and update the word current interval modifier* log ratio in the manual to make it clearer for future users if it is true?