Logarithms – Solving, Inverses, and Graphs To graph a logarithmic function simply enter it into your calculator: Graph y = log 10 x Since your calculator graphs in base 10 you would enter y = log(x)

Graph y = log 2 x Since this is not in base 10 you need to use the change of base formula that we used to find the logs and enter in: y = (log(x))/(log(2))

Solving a logarithmic function: Remember that your calculator only solves log 10 – to solve any other base you must use the change of base formula where log a b = (log(b))/(log(a)) Find log 10 25Put it into the calculator as log(25) log = Find log 6 63Put it into the calculator as (log(63))/(log(6)) log 6 63 = (log(63))/(log(6)) = Logs can also have a negative value – if the answer is a fraction Find log 2 (1/8)Put it into the calculator as (log(1/8))/(log(2)) log 2 (1/8) = (log(1/8))/(log(2)) = -3 Remember that you can check any of these answers by plugging them in as exponents and making sure you get the proper answer = 25 (or be very close) Check – log = = 25 (very close) 2 -3 = 1/8 (or be very close) Check – log 2 (1/8) = -3 1/8 = 1/8

Logs and Exponential functions are inverses So if you are asked to find the inverse of log 2 x = y log 8 x = -1 Convert it into its exponential form 8 -1 = x Log x = 6 Change it into the exponential form 2 y = x Solving a log function for a missing piece Use a calculator or thought to figure out the missing piece 8^(-1) = (1/8) or.125 (using calc) x 6 = To solve this we need to take the 6 th root of each side (x 6 )^(1/6) = (15625)^(1/6) x = 5

Homework for tonight is #39 Problem Set Corrections are due next class: Orange – Tuesday 9th Gray – Monday 8th