That’s my experience too in the engineering field.
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Good, it’s not only me then. I wonder if it’s something that comes from more applied (rather than fundamental) uses of math, maybe because of the use of “log” and “ln” on most calculators.
Same here. Log is base 10, ln is base e. That’s also what the buttons say on my scientific calculator (anyone remember them?). I just discovered there there is an ISO notation (‘lg’ for base 10), but nobody in my fields seems to care what ISO think about the matter.
I suppose log is more normally used in engineering rather than science per se, as a means of expressing wide ranges in a convenient manner. But that’s because the underlying phenomenon is logarithmic.
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On a side note how do you put somebody on ‘ignore?’ Waving math puzzles in front of an engineeer is like waving meth in front of a homeless person and I’m struggling to resist as I’m busier than a one-legged man in an ass kicking contest right now.
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Is that a serious question?
Yes. I’ve never done it before and I was hoping I could take the lazy way and have somebody just tell me.
surprised no one has mentioned forming the square.
The bit under the square root can be made into (X+Y)^2. Which because it has a square root over it cancels the squared part and leaves X+Y.
The X part is obvious, we can imagine a square of X by X. then on the right side of the square and at the bottom of the square is a slice Y wide and the length of X long and lastly there is one little box left in the bottom right which is going to be Y squared.
That’s what you get when you expand (X+Y)^2 is X^2 + 2XY + Y^2 it should also be clear that X + Y is X - 6. The square root of 36 is -6 (one of them anyway) also -6 is half of (2XY where our value is -12X) again -6 works.
Hence X = 8
The rest related to logarithms is straight forward as has been covered by others, assuming base 10 log 10 = 1, log 100 = 2, log 1000 = 3 hence the value after Log must =100
We have Log 98 + X - 6 =2 therefor X is 8
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Go to the member’s profile page, and change the status from “Normal” to “Muted” or “Ignored”
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Nice. There’s a video about this on YouTube (it’s actually about the geometric representation of quadratic equations, not imaginary numbers as such).
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My professor said that the base-10 log was originally invented for sailors.
Come to think of it, there are uses in science, so I overstepped. The Richter scale (used to measure earthquake severity) is a base-10 log. Any time you want to make numbers more presentable. The USA uses the old English system for the same logic.
I don’t recall ever seeing a base-ten log in graduate school. Natural logs are found in nature; hence the name, and you get beauties like this:
Anyway, scientific calculators notwithstanding, programs like R and Python see log() as a natural log, not a base-10 log.
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I think you can do it in the user profile page… I’ve had to do this to some users because nothing they say to me is nice.
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I always understood log as base-10 log and ln as natural log.
I don’t know why programs like R and Python don’t use this standard nomenclature instead.
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I used to think log is just log.
Like log 2 is 2 logs…
And log 1000 is enough logs to build yourself a nice fire…
And natural log is log before it got cut down…
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Solve this one!!
Why?
Sorry, I should have worded ‘no algebra’ in a more precise way. The restriction I proposed is really ‘don’t process variable ‘x’ in an explicitly algebraic expression on the paper, or any physical medium.’
For this part, it is about the quadratic equation inside the square root. Because (98+square-root(x^2 -12x +36)) = 100, the thing inside the root should be 4. So x^2-12x = -32. I didn’t want to solve the quadratic (it would be too difficult for ‘plain English’ approach. Instead, I tried to solve x (x-12) = -32.
The failure/confusion in my wording show exactly the great value of universally recognizable algebraic expression. However, no matter how convenient algebraic expression and operation are, my opinion is that we/students should not learn the instinct of diving into it before thinking it over in the head.
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logarithms were invented by Napier to simplify calculations primarily for astronomy, which had carryover to navigation, which was super useful for sailors.
pH, db for other scales off the top of my head.
that’s probably because c has log as a natural log since forever.
edit:
this is probably highly field dependent. as mentioned by others, seems pretty common in engineering that log is base 10. I wouldn’t be horribly surprised if it’s other baes than e or 10.based on field - ie in some fields of computer science it wouldn’t be a shock if it defaulted to base 2.
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Those programs are used primarily for data and statistics.
When you naturally log the data, absolute changes become percentages changes.
I can’t think of any use of base-10 logs in statistics.
R is all about stats, but Python was developed as a general purpose language and used widely; I certainly wouldn’t describe Python as primarily used for data or statistics (other than all programming languages, generally, are used for ‘data’).
it really doesn’t make much difference whether log10 or ln is used; it’s mostly just convention, and converting one to the other is trivial. that said, when dealing with e, ln is more convenient, when dealing with visualizations, log10 usually makes more sense.
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Uh, no.