1. 8/2/2013 Logarithms 1 = 2 log a x Properties of Logarithms Examples 1. log a x 2 = log a (x x) Coincidence ? log b x r = r log b x Power Rule for Logarithms = log a x + log a x

2. 8/2/2013 Logarithms 2 log b x r = log b (b r m ) Properties of Logarithms Consider log b x = m for x, b positive, b ≠ 1 log b x r = r log b x and (b m ) r = x r = r m = r log b x, for any real r Now b m = x = b rm Power Rule for Logarithms

3. 8/2/2013 Logarithms 3 log 2x Example 2. log 2x + log (x + x) + log (3x – x) Properties of Logarithms 3 Question: Is there a relationship between the = (log 2x + log 2x) + log 2x = log 4x 2 + log 2x = log 8x 3 = log (2x) Coincidence ? 3 = 3 3 exponent and the factor ? OR