The following expression called transient in Electronics, which allows you to calculate several variables such time, voltage, capacity, etc.
This is a current time function without numbers, where A is a constant, t is a time variable and T as well.
$$i(t)=A\left(1-e^{-\frac t T}\right)$$
with numbers:
$$6.32=10\left(1-e^{-\frac {-10\cdot 10^{-3}} T}\right)$$
I'd like to convert it to natural logarithm in order to get T, and I'm not sure I did it well, but I write my solution:
$$\frac{-10\cdot 10^{-3}}{\ln\left(-1\left(-1+\frac{6.32}{10}\right)\right)}=T$$
Thanks for the solution and reply, I'd be grateful for it!
Checking your solution we have
$$i(t)=A\left(1-e^{-\frac t T}\right) \iff e^{-\frac t T}=1-\frac{i(t)}A$$
then tacking natural logarithm both sides we obtain
$$-\frac t T=\log\left(1-\frac{i(t)}A\right) \iff T=-\frac{t}{\log\left(1-\frac{i(t)}A\right)}$$
and with numbers
$$T=-\frac{-10\cdot 10^{-3}}{\log\left(1-\frac{6.32}{10}\right)}$$
which agrees with your solution.