1. ## Percentage Change Operator

My finance prof is confusing me again... this time about the percentage change operator. I understand %chg = x2/x1-1, or [(x2-x1)/x1]. But can someone clarify the relationship between %chg and logs?

Here's the context:
In considering relative purchasing power parity, we have the following equation:

S(USD/EUR) x (Peur/Pus) = k for all periods

where:
Peur = Price level in EU
Pus = Price level in US
S(USD/EUR) = Spot USD price of the EUR

Now we apply the percentage chage operator (taking logs) to get:

%chgS(USD/EUR) + %chgPus - %chgPeur = 0

My sense is that this is a linear approximation....
Any help would be appreciated.
Many thx
b

2. Good call! Here is an effective resource. It confirms your "sense".

Logarithm transformation

This is a wonderfully exploitable property of logarithms:

log(a*b) = log(a) + log(b)

It is called, sometimes, linearization. Turning intractable multiplication into addition is of great value. Turning nonlinear into linear nearly is magic.