How are PPP, nominal exchange rates and inflation related?
Let $P$ denote the price in the home country, $E$ represent units
of domestic currency used to buy one unit of foreign currency, and
$P^{*}$ represent the price level in the foreign country. Now, PPP
implies that:
$$
P=EP^{*}
$$
 In other words, prices when expressed in the same currency are equalized
across countries. Log-differentiate and take changes and obtain:
$$
\hat{P}=\hat{E}+\hat{P}^{*}
$$
 where hats denote changes. Rearrange, and find that:
$$
\hat{E}=\hat{P}-\hat{P}^{*}
$$
In other words, the changes in exchange rate inform one of relative changes
in price levels (inflation). This is what is know as relative PPP