Question 150291
Is the expression {{{y=log(3,(x))}}} ???




Table of Contents:
<a name="top">
<a href="#table">Table</a>

<a href="#graph">Graph</a>



In order to plot {{{log(3,(x))}}}, we need to plot some points. To do that, we need to plug in some x values to get y values




{{{y=log(3,(x))}}} Start with the given equation.



{{{y=log(3,(1))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(2))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(3))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(4))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(5))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(6))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(7))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(8))}}} 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(3,(x))}}} Start with the given equation.



{{{y=log(3,(9))}}} 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.



<a name="table">



<a href="#top">Jump to Top of Page</a>

<h4>Table of Values:</h4><pre>

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR>TEST: 1
<tr><td>1</td><td>0</td></tr>
<tr><td>2</td><td>0.631</td></tr>
<tr><td>3</td><td>1</td></tr>
<tr><td>4</td><td>1.262</td></tr>
<tr><td>5</td><td>1.465</td></tr>
<tr><td>6</td><td>1.631</td></tr>
<tr><td>7</td><td>1.771</td></tr>
<tr><td>8</td><td>1.893</td></tr>
<tr><td>9</td><td>2</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 0),
circle(1,0,0.08),circle(1,0,0.10),
circle(2,0.631,0.08),circle(2,0.631,0.10),
circle(3,1,0.08),circle(3,1,0.10),
circle(4,1.262,0.08),circle(4,1.262,0.10),
circle(5,1.465,0.08),circle(5,1.465,0.10),
circle(6,1.631,0.08),circle(6,1.631,0.10),
circle(7,1.771,0.08),circle(7,1.771,0.10),
circle(8,1.893,0.08),circle(8,1.893,0.10),
circle(9,2,0.08),circle(9,2,0.10)

)}}}


<a name="graph">



<a href="#top">Jump to Top of Page</a>

<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=log(3,(x))}}}:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, log(3,x)),
circle(1,0,0.08),circle(1,0,0.10),
circle(2,0.631,0.08),circle(2,0.631,0.10),
circle(3,1,0.08),circle(3,1,0.10),
circle(4,1.262,0.08),circle(4,1.262,0.10),
circle(5,1.465,0.08),circle(5,1.465,0.10),
circle(6,1.631,0.08),circle(6,1.631,0.10),
circle(7,1.771,0.08),circle(7,1.771,0.10),
circle(8,1.893,0.08),circle(8,1.893,0.10),
circle(9,2,0.08),circle(9,2,0.10)

)}}} Graph of {{{y=log(3,(x))}}}