Conclusion

In summary, commit to memory these four basic rules of logarithms as given below:-

1. Log_b (mn)= log_b m + log_b n. In this rule, the multiplication of two logarithmic values is equal to the addition of their individual logarithms.

          For example, log₃ ( 2y ) = log₃ (2) + log₃ (y).

2. Log_b (m/n)= log_b m – log_b This is called as division rule. Here, the division of two logarithmic values is equal to the difference of each logarithm.

         For example, log₃ ( 2/ y ) = log₃ (2) -log₃ (y).

3. Log_b (mⁿ) = n log_b ^m

         This is the exponential rule of logarithms. The logarithm of m with a rational exponent is equal to the exponent times its logarithm.

4.  Log_b m = log_a m/ log_a b