Originally Posted by

**leilani** Graph the function: f(x) = log3(x - 3)

You can either use the definition of logs to **graph this log function**, or else use **the change-of-base formula** to convert the function into something your calculator can graph (and for which it can provide you with plot points).

The first way gives:

Code:

-------------+----------------+---------
powers | function | value of
of 3 | equation | y
-------------+----------------+---------
1/3 = 3^(-1) | log_3(1/3) = y |
x = 1/3 | 1/3 = 3^y | y = -1
-------------+----------------+---------
1 = 3^(0) | log_3(1) = y |
x = 1 | 1 = 3^y | y = 0
-------------+----------------+---------
3 = 3^1 | log_3(3) = y |
x = 3 | 3 = 3^y | y = 1
-------------+----------------+---------
9 = 3^2 | log_3(9) = y |
x = 9 | 9 = 3^y | y = 2
-------------+----------------+---------
27 = 3^3 | log_3(27) = y |
x = 27 | 27 = 3^y | y = 3
-------------+----------------+---------

The second way converts "y = log_3(x)" into "y = [ln(x)]/[ln(3)]".