SOLUTION: Plot the graph of the following function f(x) = log3^x

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Question 150438: Plot the graph of the following function
f(x) = log3^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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)



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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)



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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)



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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)


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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)




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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)



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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)




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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)




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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)



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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