Logarithms often are useful. However, if you've more than four payments, you have no expectation of solving. You may luck out, but it would be only luck.
Why would integer or non-integer make any difference? You cannot show one real example where interest rates are restricted to integer values. There are some with values rounded to integer in the end.
If your table has only integer values, you must learn to interpolate other values between them. There are many ways to do this. Linear is often sufficient.