1. ## graphs of logs

im having a bit trouble graphing logs. how do i know the shape of the graph? i know it passes through the points (1,0) along the x-axis. it goes down along the origin and what about the otherside thats going up?

like log2 is diff from log3 and is diff from log6. is there rule?

sorry my terminology is all skewed, but, do u understand what im saying?

thanks!

2. ## Re: graphs of logs

Originally Posted by noork85
im having a bit trouble graphing logs. how do i know the shape of the graph? i know it passes through the points (1,0) along the x-axis. it goes down along the origin and what about the otherside thats going up?

like log2 is diff from log3 and is diff from log6. is there rule?

sorry my terminology is all skewed, but, do u understand what im saying?

thanks!
Logarithms are inverse functions to exponentials, and exponentials are much easier to picture and graph than logarithms. So a good strategy is to graph the inverse function, then reflect it in the line y = x.

3. ## Re: graphs of logs

so lets say i have log6(x+2) what should i do first? other than knowing that my graph passes through (1,0) and theres a horizontal shift of two to the left, i duno whats going on with my graph...but then that says alot, right? i know where graph goes along the neg y-axis (downwards), but what about along the positive y-axis?

4. ## Re: graphs of logs

Originally Posted by noork85
so lets say i have log6(x+2) what should i do first? other than knowing that my graph passes through (1,0) and theres a horizontal shift of two to the left, i duno whats going on with my graph...but then that says alot, right? i know where graph goes along the neg y-axis (downwards), but what about along the positive y-axis?
I would do this...

\displaystyle \begin{align*} f: y &= \log_6{(x + 2)} \\ \\ f^{-1}: x &= \log_6{(y + 2)} \\ 6^x &= y + 2 \\ y &= 6^x - 2 \end{align*}

So graph \displaystyle \begin{align*} y = 6^x + 2 \end{align*}, then reflect it in the line \displaystyle \begin{align*} y = x \end{align*}.

5. ## Re: graphs of logs

oh, i see. okay ill do that too then. im not comfortable with a calculator yet so doing it by hand is my only option. thank u very much. will try it out and update how it goes.