[Meter]

I understand it. But why I can do so, to devide by 1 mol/ l or 1 bar, if pressure is used. A lot of websides dont consider it. And 40 years ago I went in university i also never heard it.
Its like a price is 100 $ and we devide by 1$ and say its 100. Make this sense? But I have an open ear to learn new things, if they are explained.
Sentences like :"Just because the error is common doesn't mean the idea is right" dont help.

Because quantities like the reaction quotient, pH, etc. are a measure for the activity of a certain physical property. For instance, pH measures the activity of hydrogen ions in a solution. Likewise, a reaction quotient measures the activity of molecules in a solution. All activities are dimensionless, and depending on what type of activity, your quantities have to be divided by some conversion factor, like 1 mol/L for concentrations or 1*10⁵ Pa for partial pressures.

[chenbeier]

Thanks for the explanation.

Activities and concentration are not the same like fugacities and pressure are also not the same.

[Borek]

You ignore the units part. log (nor any other function) doesn't miraculously remove units from the quantity it acts on, it can be used only on unitles quantities.

40 years ago I went in university i also never heard it.

That was definitely part of my course back in eighties, and we used books written decade or two earlier. As I already wrote - this a lousy chemistry, sadly, it is often taught without a second thought and deeper understanding of why it is wrong and inconsistent.

Just because it is popular doesn't mean it is correct.