My daughter asked me this and it stumped me. I can barely remember using them 32 years ago in college. lol. Shes confused that you can convert normal numbers to logs, and to multiply, you add, to divide, you subtract, then convert the number back again from a "log". that question even confused me. Can anyone help me out here?
What is a "logarithm"?
- Thread starter pieman109
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log usually means log to the base 10. I say it in my head as:
log100 = what power of 10 equals 100?
log100 = 2
There are lots of rules surrounding logs which can be extremely useful in certain situations. Wikipedia is bound to have a good page on logs.
log100 = what power of 10 equals 100?
log100 = 2
There are lots of rules surrounding logs which can be extremely useful in certain situations. Wikipedia is bound to have a good page on logs.
p4radox said:
That's correct - although what base you're talking about depends on the context. In computer science, it's usually 2, in mathematics it's usually e (natural logs), in other circumstances it's sometimes 10. A subscript can be written to specify the base.
Particular laws worth knowing:
log(ab) = log(a) + log(b) (easy to demonstrate from the definition)
This means that to multiply a and b, you can find the logarithm of these, add them, then look for the "inverse log" to find a*b. In the days before calculators this was a simple way of multiplying numbers - these days they don't tend to come up until A-level.
also: log(a^n) = n*log(a) - which makes them useful for powers as well. (ie. to find a^n, find the log of a, multiply it by n (maybe using the rule above), then find the inverse of the log.
However, the above isn't much used anymore - after all, you can just use a calculator, so it's not really taught except as a "that's how people used to do it" sidenote. Natural logs come up in loads of places though - as the inverse of e^x in differential equations and integrals all over the place.
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Soldato
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Logarithms are the inverse of exponentials:
logb(x) = y <=> b^y = x
As for multiplication rules, etc.:
alog(x) = log(x^a)
log(x/y) = log(x) - log(y)
log(xy) = log(x) + log(y)
Those are the basics of logs
logb(x) = y <=> b^y = x
As for multiplication rules, etc.:
alog(x) = log(x^a)
log(x/y) = log(x) - log(y)
log(xy) = log(x) + log(y)
Those are the basics of logs
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Associate
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What p4radox said. For what your daughter seems to be confused with:
loga(b) = c
Can be rewritten as
a^c=b
And the simple rules:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b*log(a)
loga(b) = c
Can be rewritten as
a^c=b
And the simple rules:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b*log(a)