Opamp logarithmic & exponential amplifiers

So I was playing around with logarithmic & exponential amplifiers in my lab class. I was looking at the following equations:

Experimentally I found out that if I feed in 0V in both log. and exp. amplifiers I get 0V output.
But according to the equations the log of zero is undefined and the power of any number is one, i.e. I should never get zero output voltage.
I was wondering how to explain this observation, was it that my experiment was flawed or that real life op amps behave differently than those equations predict?

$$I = I_s [exp( \frac{V}{nV_T} )- 1]$$ where V is the applied voltage, ##I_s## is the saturation current and ##V_t## is "thermal voltage", that is, ## k_B T/e## (Boltzmann constant x absolute temperature /elementary charge). So, when V is a few times greater than ##V_T##, the equation simplifies to $$I = I_s [exp( \frac{V}{nV_T} )- 1] \approx I_s exp( \frac{V}{nV_T} )$$ and that's the range of voltages where these circuit work as logarithmic or exponential amplifiers. But when V gets close to zero, the effects of the constant term in the first equation is not negligible.