Logarithms – Solving, Inverses, and Graphs
To graph a logarithmic function simply enter it into
your calculator:
Graph y = log10x
Since your calculator graphs in base 10 you would
enter y = log(x)
Graph y = log2x
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 log10 – to solve any
other base you must use the change of base formula where
logab = (log(b))/(log(a))
Find log1025 Put it into the calculator as log(25)
log1025 = 1.398
Find log663
Put it into the calculator as (log(63))/(log(6))
log663 = (log(63))/(log(6)) = 2.312
Logs can also have a negative value – if the answer is a fraction
Find log2(1/8) Put it into the calculator as (log(1/8))/(log(2))
log2(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
Check – log1025 = 1.398
101.398 = 25 (or be very close)
25.003 = 25 (very close)
Check – log2(1/8) = -3
2-3 = 1/8 (or be very close)
1/8 = 1/8
Logs and Exponential functions are inverses
So if you are asked to find the inverse of log2x = y
Change it into the exponential form 2y = x
Solving a log function for a missing piece
log8x = -1
Convert it into its exponential form
8-1 = x
Use a calculator or thought to figure out the
missing piece
8^(-1) = (1/8) or .125 (using calc)
Logx15625 = 6
x6 = 15625
To solve this we need to take the 6th root of each side
(x6)^(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