|1. In N and a (¹1) are any two positive real numbers and for some real x, ax = N, then x is said to be the logarithm of N to the base 'a'.
2. ax = N is an exponential function and the corresponding logarithmic function is x = logaN.
3. alogaN = 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. logxab = logxa + logxb.
8. logx(a/b) = logxa - logxb.
9. logxa = logya + logxy [This is known as change of base of a log].
10. logxy = logxa / logya or logxy = logay / logax.
11. logxnym = m/n log xy.
12. log ap.bq = 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 = ax, then logaN = x.
2. Log a 1 = logx 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 = logbN - log ab.