Logs help

[Nash]

My girlfriend asked me a question for her revision for her exam soon and I can't do it. Can someone help me please?

According to the formula what is the length of a fish of mass 200 g predicted to be?
(The linear form is: log W = log a + b log L). (2 marks)
Where a and b are parameters, a = 3.63x10-6, b = 3.2.

I am pretty sure it's:

log W - log a = b log L

How do I get just L on its own?

log W - log a
--------------- = L
e^b

Is that right?

Thanks

 

[davethe11]

10 ^ ( (log W - log a) / b ) = L

hold on, let me check...


[edit] yeah, think thats right


divide both sides by b first, then raise both to the power of ten (I assume your using the common logarithm)

10 ^ log(base 10) Z = Z

therefore:

10 ^ log L = L


oops, I see you've used e, your using ln, hold on a mo.........

and now I'm confused lol I think your just using the common logarithm so just punch in the values

 

[Nullvoid]

Would this be a possible alternative?

log W = log a + b log L
log W = log a + log L^b (since x log y = log y^x)
log W = log (aL^b) (log x + log y = log (xy))
W = aL^b (the logs can be dropped since you have a single term on each side)
L^b = W/a

And umm, I can't write out the last one since I can't put the proper symbols in, but it would be (W/a) inside a root symbol with the value of b.

 

[p4radox]

Would this be a possible alternative?

log W = log a + b log L
log W = log a + log L^b (since x log y = log y^x)
log W = log (aL^b) (log x + log y = log (xy))
W = aL^b (the logs can be dropped since you have a single term on each side)
L^b = W/a

And umm, I can't write out the last one since I can't put the proper symbols in, but it would be (W/a) inside a root symbol with the value of b.

That's pretty much how I'd do it.

LogW - Loga = bLogL
Log(W/a) = bLogL
Log(W/a) = LogL^b
W/a = L^b

Therefore L = (W/a)^(1/b)

 

[davethe11]

^^ what they said

 

[Nash]

Cool, thanks for the help