document.write( "Question 173131: Graph f(x) = log3x \n" ); document.write( "

Algebra.Com's Answer #127982 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"f%28x%29=log%283%2C%28x%29%29\"$ , we need to plot some points:\r
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\n" ); document.write( "\n" ); document.write( "Note: I'll use \"y\" in place of f(x)\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \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( " $\"y=0\"$ Use a calculator to evaluate log base 3 of 1 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , then $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \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( " $\"y=0.63093\"$ Use a calculator to evaluate log base 3 of 2 to get 0.63093\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , then $\"y=0.63093\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \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( " $\"y=1\"$ Use a calculator to evaluate log base 3 of 3 to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , then $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \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( " $\"y=1.26186\"$ Use a calculator to evaluate log base 3 of 4 to get 1.26186\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , then $\"y=1.26186\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=5\"$ \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( " $\"y=1.26186\"$ Use a calculator to evaluate log base 3 of 5 to get 1.46497\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , then $\"y=1.46497\"$ \r
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\n" ); document.write( "\n" ); document.write( "So we have the following values:\r
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x	y
1	0
2	0.63093
3	1
4	1.26186
5	1.46497

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\n" ); document.write( "\n" ); document.write( "Now let's plot these points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through those points to graph $\"f%28x%29=log%283%2C%28x%29%29\"$ \r
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