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

Algebra ->  Exponential-and-logarithmic-functions -> 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      Log On


   

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) About Me  (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:
+graph%28+300%2C+200%2C+-1%2C+8%2C+-2%2C+3%2C+log%283x%29+%29+
:
:
Did this make sense to you?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression y=log%283%2C%28x%29%29 ???



Table of Contents:

Table
Graph


In order to plot log%283%2C%28x%29%29, we need to plot some points. To do that, we need to plug in some x values to get y values



y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%281%29%29 Plug in x=1


y=0 Evaluate the right side with a calculator


So when x=1, y=0 which makes the point (1,0)



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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%282%29%29 Plug in x=2


y=0.631 Evaluate the right side with a calculator


So when x=2, y=0.631 which makes the point (2,0.631)



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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%283%29%29 Plug in x=3


y=1 Evaluate the right side with a calculator


So when x=3, y=1 which makes the point (3,1)



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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%284%29%29 Plug in x=4


y=1.262 Evaluate the right side with a calculator


So when x=4, y=1.262 which makes the point (4,1.262)


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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%285%29%29 Plug in x=5


y=1.465 Evaluate the right side with a calculator


So when x=5, y=1.465 which makes the point (5,1.465)




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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%286%29%29 Plug in x=6


y=1.631 Evaluate the right side with a calculator


So when x=6, y=1.631 which makes the point (6,1.631)



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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%287%29%29 Plug in x=7


y=1.771 Evaluate the right side with a calculator


So when x=7, y=1.771 which makes the point (7,1.771)




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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%288%29%29 Plug in x=8


y=1.893 Evaluate the right side with a calculator


So when x=8, y=1.893 which makes the point (8,1.893)




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

Let's find another point


y=log%283%2C%28x%29%29 Start with the given equation.


y=log%283%2C%289%29%29 Plug in x=8


y=2 Evaluate the right side with a calculator


So when x=9, y=2 which makes the point (9,2)



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

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





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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:







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Graph:


Now draw a curve through all of the points to graph y=log%283%2C%28x%29%29:


Graph of y=log%283%2C%28x%29%29