Graphing log functions!?

[ericaveronica]

Hi there. I need help! I need to know how to manually graph log functions. But not just the base 10 ones... I need to know how to graph logs of any base and how to find the intercepts and asymptotes. please help! :!:

 

[Gene]

This looks like a good place to start.
http://www.purplemath.com/modules/graphlog.htm
----------------
Gene

 

[soroban]

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.

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[pka]

"You will find that all log functions of the form: $\displaystyle y = \log _b (x)$.have the same graph."
This is not the case!
That is true only if b>1. If 0<b<1 then the graph looks like:

 

[soroban]

Picky! Picky!

But you're right, of course . . .