Interpreting negative binomial regression with log transformed independent variables

#1
My independent variables were highly skewed, so to normalise the distribution they were log transformed. Also since there were zeros in the data, I've added + 1 to transform the variables. This is what the model looks like (negative binomial regression):

Dependant_var ~ log(Independent_var_1 + 1) + log(Independent_var_2 + 1)

Coefficients:
Est. Std. Err. z-value sig.
log(Independent_var_1 + 1) 0.031907 0.004701 6.787 1.14e-11 ***
log(Independent_var_2 + 1) -0.019007 0.004735 -4.015 5.96e-05 ***

IRRs:

log(Independent_var_1 + 1) 1.0324219
log(Independent_var_2 + 1) 0.9811724


Now, I'm having problems understanding how to interpret the results. If the data were not log transformed, I would interpret this as follows:

If everything else is held constant, a one unit increase in Independent_var_1 would result in the decrease by 0.031 units of Dependent_var. And for IRRs – a one unit increase of Independent_var_1 will result in an expected increase of the Dependent_var by a factor of 1.032 (everything else constant).

However, I'm confused since I don't have "units" anymore, but log transformed vars. Thanks.
 
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