Question

logarithm help..... anyone..

how do you expand log(3v/w^2) ??

Answer 1

Did you try?

Answer 2

did i try what.. i dont know how to do it..

Answer 3

do you remember you can change division inside a log to subtracting logs:
log(a/b)= log(a)-log(b)
so if you match 3v to a and w^2 to b, can you re-write the log as subtraction?

Answer 4

when i write that out, is that expanded fully

Answer 5

no, but the way to do these problems is step by step. What did you get?

Answer 6

log(3v/w2)=log(3v)-log(w2)

Answer 7

yes. Now the other rule: you can change multiplication inside a log to adding logs:
log(ab)= log(a)+log(b)
so, match 3 to a and v to b, and rewrite log(3v) as the sum of two logs.

Answer 8

so log(3v) = log(3) + log (b)

Answer 9

log(v)*

Answer 10

yes, if you mean log(3) + log(v) (we match a to 3 and v to b to use the rule)
Now -log(w^2)
we can rewrite w^2 as w*w and use the same multiplication rule:
-( log(w)+ log(w))
which is the same as -2log(w) (add them up, then multiply by the -1 out front)

final answer: log(3)+ log(v)-2log(w)

Answer 11

whoa. ok so sometimes we have to use multiple properties to get the expansion..

Answer 12

or we could use a 3rd rule:
log(a^n) (a to the nth power) = n log(a)
using this rule:
-log(w^2)= -2log(w) (as it should be)

so those are pretty much the only rules you need to learn to do these problems

Answer 13

If you practice, it gets easier.

Answer 14

with this third rule,
what do i need to do with -log(w^2)=-2log(w)

Answer 15

the 2 in w^2 is the exponent. you move the exponent out of the log, and multiply by it.
log(a^n) --> n*log(a)

is is short-hand for doing this:
say n=4 (as an example) a^4 = a*a*a*a (a times itself 4 times)
log(a^4)= log(a*a*a*a)= log(a)+log(a)+log(a)+log(a)= 4log(a)

Answer 16

ok that makes sense. ill need to practice. thanks a lot

Answer 17

good luck!