The formula you posted is for simple kriging, not ordinary kriging. The formula for ordinary kriging looks similar, but it uses a Lagrange multiplier, which makes it a lot harder to understand.
For simple kriging, if you want to get the expected value and variance in the log-space (before the back transformation), then you should do the transformation manually. Create a new field in your feature class, and calculate the log of the data with the Field Calculator. Then perform simple kriging (with no transformation) on the logged data. The prediction surface will correspond to the estimated value, and the prediction standard error surface corresponds to the square root of the estimated variance.