FP3 Help Maclaurins

Hi, a questions has asked me to show that ln(1+e^x)=ln2+1/2x+1/8x^2 which I managed

but then the next part which is just one mark asks to show what ln((1+e^x)/2) is and in the mark scheme it says it's 1/2x+1/8x^2 could anyone explain why thats the answer.

Thanks!!!

$\ln \left(\dfrac{1+e^x}{2}\right) \equiv \ln (1+e^x) - \ln 2$.