SOLUTION: How do you graph f(x)=log3x? I am so confused I don't even know where to begin. I need help with showing what this would look like on a graph. I would like to say th

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Question 150291: How do you graph f(x)=log3x?


I am so confused I don't even know where to begin. I need help with showing what this would look like on a graph.


I would like to say thank you in advance to anyone who can help me graph this. I am really grateful for your help.

Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
How do you graph f(x)= log 3x?
:
y = f(x)
then
y = log(3x)
:
WE can't have log of zero or a neg number therefore all values: x > 0
:
Start with x = .22, using a calc, enter log(3*.2) = -.22
x = .6; log(3*.6) = +.25
x = 1; log(3*1) = +.48
x = 1.4 log(3*1.4) = +.62
:
After this the curve flattens out so we can jump to x = 2
x = 2 log(3*2) = .78
x = 4 log(3*4) = 1.08
Continuing like this make a table
x | y
-------
.2 |-.22
.6 |+.26
1.0|+.48
1.4|+.62
2.0|+.78
4.0|1.08
6.0|1.26
:
Plot this on graph, scaled about like this:

:
:
Did this make sense to you?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Is the expression ???



Table of Contents:

Table
Graph


In order to plot , we need to plot some points. To do that, we need to plug in some x values to get y values



Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (1,0)



--------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (2,0.631)



-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (3,1)



-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (4,1.262)


-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (5,1.465)




-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (6,1.631)



-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (7,1.771)




-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (8,1.893)




-------------------------------

Let's find another point


Start with the given equation.


Plug in


Evaluate the right side with a calculator


So when , which makes the point (9,2)



========================================================

Now let's make a table of the values we just found.





Jump to Top of Page

Table of Values:


TEST: 1



xy
10


20.631


31


41.262


51.465


61.631


71.771


81.893


92

Now let's plot the points:







Jump to Top of Page

Graph:


Now draw a curve through all of the points to graph :


Graph of

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