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