SOLUTION: How do you graph a logarithmic function in easy-to-understand steps? I must be able to graph problems such as y = log 1/3 (1/3 is the base of the logarithm) x-1 ... y = log1/3 x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do you graph a logarithmic function in easy-to-understand steps? I must be able to graph problems such as y = log 1/3 (1/3 is the base of the logarithm) x-1 ... y = log1/3 x      Log On


   

Question 36162: How do you graph a logarithmic function in easy-to-understand steps? I must be able to graph problems such as
y = log 1/3 (1/3 is the base of the logarithm) x-1 ... y = log1/3 x-1
y = log5 (5 is base of the logarithm) (x+2) ... y = log5 (x+2)
Why does one have parentheses and one doesn't? Does that make a difference? PLEASE HELP! ASAP! QUIZ TOMORROW AND I DON'T KNOW HOW TO GRAPH! THANKS!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you graph a logarithmic function in easy-to-understand steps? I must be able to graph problems such as
y = log 1/3 (1/3 is the base of the logarithm) x-1 ... y = log1/3 x-1
y = log5 (5 is base of the logarithm) (x+2) ... y = log5 (x+2)
Why does one have parentheses and one doesn't?
y = log1/3 (x-1)
Plot some points to see the graph:
Let x=4/3 then y=log(base 1/3) of 1/3 =1
Let x=2 then y=0
Let x=4 then y=-1
Let x=10 then y=-2
How to do this?
Rewrite as (1/3)y=x-1
Put values in for y and solve for x.
y = log5 (x+2)
Let x=3 then y=1
Let x=23 then y=2
Let x=123 then y=3
How can you see this?
Change to an exponential equation, as follows:
5^y=(x+2)
Put in some values for y and solve for x
The parentheses help you make sure where the anti-log starts and finishes.
logx+1 is confusing as you don't know if you mean (logx)+1 of log(x+1)
Cheers,
stan H.