How do you read currency exchange rates in terms of domestic and foreign currency?
The currency in the denominator is always the currency that is being priced. For example $\$/€=x$ means that the price of euros is $x$ dollars. That is, if you want $1$ euro, you have to pay $x$ dollars (Keep in mind that in practice the euro will have a bid and an ask price, but in both cases, the euro will be in the denominator). In fact, the notation $\$/€$ should be read "dollars per euro". In contrasts, $€/\$$ reads "euros per dollar", so the currency that is being priced now is the dollar (of course in terms of euros). 

With this in mind, the statement online that says "E$\$/€ = 1.50$, [...] would mean that $1\$$ would buy $1.50€$". was either misunderstood or simply wrong. Such notation means that $1.50\$$ is equivalent to $1€$.

Finally, keep in mind that, in practice, countries decide to write their exchange rate in terms of the dollar according to convenience of the numbers. For example, the exchange rate for the Mexican peso is almost always written as peso/dollar. Technically speaking such notation is giving the price of dollars, but note that it is more convenient to say that E$(peso/dollar)=24$ pesos rather than saying E$(dollar/peso)=0.041666$ dollars. This creates no problem since both quotes are equivalent.