2. a^x = N is an exponential function and the corresponding logarithmic function is x = log_aN.

3. a^log_aN = N.

4. The logarithm of the same number to different bases are different.

5. The logarithm of unity to any any non zero base is zero.

6. The logarithm of any non-zero positive number to the same base is unity.

7. log_xab = log_xa + log_xb.

8. log_x(a/b) = log_xa - log_xb.

9. log_xa = log_ya + log_xy [This is known as change of base of a log].

10. log_xy = log_xa / log_ya or log_xy = log_ay / log_ax.

11. log_xⁿy^m = m/n log _xy.

12. log a^p.b^q = p log a + q log b.

13. Logarithm of number contain, integral and decimal parts, the integral part of the logarithm of a number is called the "characteristic" and the decimal part is "mantissa".

14. If the number has 'n' digits the characteristic of its logarithm is 'n-1' digits.

15. If the characteristic of the logarithm is n, the number will have 'n+1' digits.

1. If N = a^x, then log_aN = x.

2. Log _a 1 = log_x 1 = log₅ 1 = 0.

3. Log _aa = 1.

4. Log MN = log M + log N.

5. log(M/N) = log M - log N.

6. log xⁿ = n log x.

7. log _a N = log_bN - log _ab.