Back transform mixed-effects model's regression coefficients for fixed-effects from log to original scale

Question

I am running a mixed-effects model with the lme4 package. The model specifications are: log(dv) ~ 1 + A*B*C + (1+A*B|random1) + (1+A|random2), where A and B are within-group conditions and C is a between-group condition.

The first problem is that the coefficients for fixed effects are on the log scale and only the intercept makes sense when I do exp(coef) (see below).

The second problem is even if I do an exponentiation transform, how should I account for the random-effects structure? As I understand it, the random-effects structure affects the fixed-effects coefficients (I might be wrong here).

This is a sample output of my fixed-effects coefficients:

            Estimate
(Intercept) 6.533079
A1          0.062171
A2          0.077409
B1         -0.184366
B2         -0.154115
C           0.152238
A1:B1      -0.015494
A2:B1      -0.017655
A1:B2       0.001674
A2:B2      -0.003641
A1:C        0.013021
A2:C        0.038995
B1:C        0.010087
B2:C        0.013721
A1:B1:C     0.016025
A2:B1:C     0.016453
A1:B2:C     0.012746
A2:B2:C     0.003113

Now, exp(6.533079) gives 687.5118, which makes sense in the original scale, but the rest of the numbers do not make sense once transformed.