document.write( "Question 150291: How do you graph f(x)=log3x? \r
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Algebra.Com's Answer #110358 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Is the expression $\"y=log%283%2C%28x%29%29\"$ ???\r
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\n" ); document.write( "\n" ); document.write( "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\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%28x%29%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%281%29%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=0\"$ which makes the point (1,0)\r
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\n" ); document.write( "\n" ); document.write( "Let's find another point\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%28x%29%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%282%29%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.631\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=0.631\"$ which makes the point (2,0.631)\r
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\n" ); document.write( "\n" ); document.write( "Let's find another point\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%28x%29%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%283%29%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"y=1\"$ which makes the point (3,1)\r
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\n" ); document.write( "\n" ); document.write( "Let's find another point\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%28x%29%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%284%29%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.262\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"y=1.262\"$ which makes the point (4,1.262)\r
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\n" ); document.write( "\n" ); document.write( "Let's find another point\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%28x%29%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%285%29%29\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.465\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"y=1.465\"$ which makes the point (5,1.465)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%286%29%29\"$ Plug in $\"x=6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.631\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=6\"$ , $\"y=1.631\"$ which makes the point (6,1.631)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%287%29%29\"$ Plug in $\"x=7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.771\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=7\"$ , $\"y=1.771\"$ which makes the point (7,1.771)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%288%29%29\"$ Plug in $\"x=8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.893\"$ Evaluate the right side with a calculator\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=8\"$ , $\"y=1.893\"$ which makes the point (8,1.893)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=log%283%2C%289%29%29\"$ Plug in $\"x=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=9\"$ , $\"y=2\"$ which makes the point (9,2)\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "TEST: 1\r\n" );
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document.write( "x y
1 0
2 0.631
3 1
4 1.262
5 1.465
6 1.631
7 1.771
8 1.893
9 2\r\n" );
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Graph:

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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=log%283%2C%28x%29%29\"$ :\r
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Graph of $\"y=log%283%2C%28x%29%29\"$
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