PRECALCULUS I PROPERTIES OF LOGARITHMS Dr. Claude S. Moore Danville Community College

CHANGE OF BASE for positive real numbers a, b, and x such that a  1 and b  1.

PROPERTIES OF LOGARITHMS 1. log b (uv) = log b u + log b v. 2. log b (u/v) = log b u - log b v. 3. log b u n = n log b u.

PROPERTIES OF NATURAL LOGARITHMS 1. ln (uv) = ln u + ln v. 2. ln (u/v) = ln u - ln v. 3. ln u n = n ln u.

EXPMPLE: CHANGE OF BASE

EXAMPLE: EXPAND LOG EXPRESSION

EXAMPLE: CONDENSE LOG EXPRESSIONS

EXAMPLE: Find the exact value of log 8 2.

LET US WORK EXAMPLES.