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# Logarithmic change watch

1. Hi,

I have a problem that has been plaguing me for the last couple of days but I still can't work it out - I'm sure this is pretty straightforward but my maths seems to be a little rusty. I would appreciate anyone that can help me out here as this is for my dissertation.

If their are two equations:

log(a)=tlog(b)+ulog(c)+vlog(d) + w

log(d)=xlog(e)+y(f)+ z

where a, b, c, d, e, f are variables and t, u, v, w, y, z are constants

Note that f is not in logarithmic form, how can I calculate what percentage change a 1% increase in f would cause a?

Many thanks
2. Substitute the second equation into the first, then rearrange for a alone on the LHS, then calculate , where a(f) is the expression you calculated for a in terms of all the other variables including f. (I'm using a(f) as a function, not multiplication.) Then you can divide one by the other to get the ratio change.

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Updated: May 12, 2013
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