Hello, ericaveronica!
I need to know how to <u>manually</u> graph log functions.
But not just the base 10 ones.
If you want to plot the points "by hand", you need the Base-change Formula:
.\(\displaystyle \log_b(N) \;= \;\frac{\log(N)}{\log(b)}\)
. . The right side can use any base.
.(I'll use base ten.)
<u>Example</u>:
.\(\displaystyle y\;=\;\log_5(x)\)
Some of the points are:
. . \(\displaystyle x\,=\,0.001:\;y\,=\,\log_5(0.001)\,=\,\frac{\log(0.001)}{\log(5)}\,=\,-4.292\)
. . .\(\displaystyle x\,=\,0.01:\;y\,=\,\log_5(0.01)\,=\,\frac{\log(0.01)}{\log(5)}\,=\,-2.861\)
. . . \(\displaystyle x\,=\,0.1:\;y\,=\,\log_5(0.1)\,=\,\frac{\log(0.1)}{\log(5)}\,=\,-1.431\)
. . . . \(\displaystyle x\,=\,1:\;y\,=\,\log_5(1)\,=\,\frac{\log(1)}{\log(5)}\,=\,0\)
. . . . \(\displaystyle x\,=\,2:\;y\,=\,\log_5(2)\,=\,\frac{\log(2)}{\log(2)}\,=\,0.431\)
. . . . \(\displaystyle x\,=\,3:\;y\,=\,\log_5(3)\,=\,\frac{\log(3)}{\log(5)}\,=\,0.683\)
. . . . \(\displaystyle x\,=\,4:\;y\,=\,\log_5(4)\,=\,\frac{\log(4)}{\log(5)}\,=\,0.861\)
. . . .\(\displaystyle x\,=\,20:\;y\,=\,\log_5(20)\,=\,\frac{\log(20)}{\log(5)}\,=\,1.861\)
. . . .\(\displaystyle x\,=\,50:\;y\,=\,\log_5(50)\,=\,\frac{\log(50)}{\log(5)}\,=\,2.431\)
But you should do this only
once.
You will find that <u>all</u> log functions of the form: \(\displaystyle y\,=\,\log_b(x)\)
.have the same graph.
Code:
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