Interpreting negative binomial regression with log transformed independent variables

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)

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 ***


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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