amath

Laws of Logarithms


First, work through this investigation to discover the laws of logarithms for yourself.
The laws of logarithms are closely related to the laws on exponents:

If M and N are positive real numbers and b is a positive number other than 1, then:
  1. log_b MN = log_b M + log_b N
  2. log_{b} (M/N)=log_b M - log_b N
  3. log_b M = log_b N iff M = N
  4. log_b M^k = k log_b M , for any real number k



Using these laws,we can simplify expressions, solve equations and inequalities. Here are some examples:


Example 1 Simplify 2 log a - log b - 3 log c




Example 2. Simplify log (1/2) + log (2/3) + log (3/4) + ... + log (99/100)





Click here for logarithmic equations.

endamath