No, that's not correct in the slightest.
> pops up in finance only when you're talking about Bitcoin
If you are looking at linear stock value graphs you are being mislead. If you want to make correct decisions based on graphs they must be logarithmic (except percent graphs). Any stock trader that uses linear graphs will lose his shirt. (And I am well aware that the default stock graphs are all linear.)
> you only would want log graphs for exponential growth or decay
No, that's not correct (for the common meaning of exponential meaning "huge"). You want a logarithmic graph anytime the future value of something depends on the present value (i.e. the mathematical meaning). Which is most of the time. Most things in the world, the amount you have today influences how much you will have tomorrow.
It's actually rare to want a linear graph. You only want that when how much you have tomorrow has nothing to do with today.
So population should be logarithmic (the more people you have the more will be born), but infant mortality per capita should be linear (future levels of infant mortality do not depend on how many died in the past).