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:

- log_b MN = log_b M + log_b N
- log_{b} (M/N)=log_b M - log_b N
- log_b M = log_b N iff M = N
- log_b M^k = k log_b M , for any real number
*k*

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

step endamath 1 : amath log a^2-log b - log c^3

step endamath 2 : amath log (a^2 / (b c^3))

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

step endamath 1 : amath log ( 1/2 xx 2/3 xx 3/4 xx ... xx 99/100 )

step endamath 2 : amath =log (1/100)

step endamath 3 : amath =-2