How to reconsider MSE metric when doing target engineering through a logarithm?
You have a $Y_{true}$
Then you calculated $Y^{log}_{true}$
So, your predictions are $Y^{log}_{pred}$
Then you can calculate the $MSE^{log}$ but it can't be compared with 100 MSE.
So, you can do a - $base^{MSE^{log}}$
to make it comparabale to 100 MSE.
A better intuitive approach will be to convert back your $Y^{log}_{pred}$
 i.e. $base^{Y^{log}_{pred}}$
Then calculate the MSE
The inverse of log is just about using power to the base
import numpy as np
input = np.array([100, 1000])
log_out = np.log10(input)

input_re = 10**(log_out)
input_re