I am so new in using R and edgeR. I calculated the logFC in edgeR using the following code:

targets <- read.delim("cell_line_M.txt", stringsAsFactors = FALSE)

d <- readDGE(targets)
colnames(d) <- c("MG1","MG2", "MN1","MN2")
d <- estimateCommonDisp(d, verbose=TRUE)
d <- estimateTagwiseDisp(d, trend="none")

et <- exactTest(d,pair=c("MN","MG"))
print(et)

this is what I obtained :

          logFC   logCPM       PValue
A1CF  0.20103589 4.718215 0.8603790511

my problem is how the logFC is calculated. the main file is

gene   MG1  MG2  MN1 MN2
A1CF    8   7    7   4

I expect that the logFc should be calculated from the strategy suggested in here like:

FC=sqrt(87)/ sqrt(74) --> logFC=log2(FC) = 0.49

but edgeR suggest logFC=0.2

Can anyone guide me if in a wrong way I am or i missed anythong?

The logFCs are calculated in a much more sophisticated way. It requires fitting a NB generalized linear model and then estimating the coefficients. You can't simply use the raw counts for computing logFCs without taking into account other factors such as the library sizes, the dispersion estimates, etc.