document.write( "Question 173334: I could really use some help graphing these two functions:
\n" ); document.write( "f(x)=7^x \r
\n" ); document.write( "\n" ); document.write( "f(x)= log3x \n" ); document.write( "

Algebra.Com's Answer #128176 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=7%5Ex\"$ , 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 $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5E%28-2%29\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F7%29%5E2\"$ Flip the fraction to make the exponent positive.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2F49\"$ Square $\"1%2F7\"$ to get $\"1%2F49\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.02041\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , then $\"y=0.02041\"$ \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( " $\"y=7%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5E%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F7%29%5E1\"$ Flip the fraction to make the exponent positive.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2F7\"$ Raise $\"1%2F7\"$ to the first power to get $\"1%2F7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.14286\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , then $\"y=0.14286\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5E%280%29\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Raise $\"7\"$ to the zeroth power to get $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , then $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "------------------------------------------------------------------\r
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\n" ); document.write( "
\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( "\n" ); document.write( " $\"y=7%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7%5E%281%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=7\"$ Raise $\"7\"$ to the first power to get $\"7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , then $\"y=7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So we have the following values:\r
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x	y
-2	0.02041
-1	0.14286
0	1
1	7

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\n" ); document.write( "\n" ); document.write( "Now let's plot these points\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through those points to graph $\"f%28x%29=%281%2F5%29%5Ex\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( "Note: the graph does NOT cross or touch the x-axis. It just looks like that since the y values become very small.\r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( "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 draw a curve through those points to graph $\"f%28x%29=log%283%2C%28x%29%29\"$ \r
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