Log-linearisation of the aggregate price

Hello everyone!
I construct a DSGE model which have two different products, the prices of the two products are p1t and p2t respectively, so the aggregate price is Pt, when I log-linearize the aggregate price Pt, I get the formula as follows: Pt_log_linearisation. However when I read the other’s paper, I find their log-linearisation of aggregate price is different from mine, their log_linearisation formula is Pt_log_linearisation2
I am a little confused about the log-linearisation of aggragate price, are the three prices p, p1, p2 equal when they are in equilibrium? but I can’t get the conslusion p=p1=p2 when solving the steady state of the model. Could you explain it to me?
Thank you !

In most models, sectors are symmetric (identical preferences and technology), making their prices equal.

I got it, thank you for your explaining~:blush: