Dimensional Analysis and units of voltage

[Nusc]

Homework Statement

The first equation below has units of voltage.

Homework Equations

$$V(t)=IR(1-e^{t/RC}) \rightarrow ln|IR - V(t)| = ln|IR|-t/RC$$

The Attempt at a Solution

the logarithm has units of voltage, but what does ln|IR| and ln|V| physically mean?

 

[Nusc]

The purpose of this question is that if you plot the natural logarithm of the voltage versus time, it should yield a straight line with slope -1/RC and intercept ln|V_c|.

From which you can determine the capacitance given a known resistance. Or maybe I should post this in the general physics forum?