1. ## word problem

Let $f(x)=ln(\frac{x}{(x^2-25)^3})$

Johnny graphs f(x) by entering in the right hand side of the previous equation into his graphing calculator because his teacher told him it would be easier ( less parenthesis and such). Is this method good advice? why or why not?

I don't understand why, how and etc.

2. Did you repeat the question word for word, because you should? You're question sort of confuses me. To answer it, yes, graphing $ln(\frac{x}{(x^2-25)^3})$ would produce the graph of the function. Of course the plot window must be set so that you can see the curve. I don't understand what is ment by fewer parenthesis? Is this a question where you are given the instructions once and you do them for a), b) c), d)...?

3. Originally Posted by superdude
Did you repeat the question word for word, because you should? You're question sort of confuses me. To answer it, yes, graphing $ln(\frac{x}{(x^2-25)^3})$ would produce the graph of the function. Of course the plot window must be set so that you can see the curve. I don't understand what is ment by fewer parenthesis? Is this a question where you are given the instructions once and you do them for a), b) c), d)...?

That is what I don't understand by (fewer parenthesis). I also don't understand by entering from right hand side.

4. Can you take a picture or scan the question from your text book and post it?

5. Originally Posted by superdude
Can you take a picture or scan the question from your text book and post it?

That is the exact question:
a. $Let f(x) = ln(\frac{x}{(x^2-25)^3})$
b. $Let f(x) = ln(\frac{x}{(x^2-25)^3}) = ln(x)-3ln(x-5)-3ln(x+5)$

Johnny graphs f(x) by entering in the right hand side of the previous equation into his graphing calculator because his teacher told him it would be easier (less parentheses and such). Is this method good advice? why or why not?

I think he was referring to (b.) right hand side. they are much the same but I don't know which is more easier. for me I can do both. Which one would think is easier to use on calculator? why or why not?

6. Originally Posted by Anemori
That is the exact question:
a. $Let f(x) = ln(\frac{x}{(x^2-25)^3})$
b. $Let f(x) = ln(\frac{x}{(x^2-25)^3}) = ln(x)-3ln(x-5)-3ln(x+5)$

Johnny graphs f(x) by entering in the right hand side of the previous equation into his graphing calculator because his teacher told him it would be easier (less parentheses and such). Is this method good advice? why or why not?

I think he was referring to (b.) right hand side. they are much the same but I don't know which is more easier. for me I can do both. Which one would think is easier to use on calculator? why or why not?
The problem makes a lot more sense when parts aren't missing...

So, we know ln(xy) = ln(x) + ln(y), and ln(x/y) = ln(x) - ln(y), and we can check that equation (b) presents a valid decomposition from these rules.

The only thing we need to be careful about is domain as we can only take logarithms of positive values.

Note that the RHS of equation (b) works as long as x > 5.

Now we check x/((x^2-25)^3) > 0

In fact this becomes x > 5 OR -5 < x < 0.

So if Johnny uses the RHS expression, he will be missing the part of the graph where -5 < x < 0.

7. Thank you that was greatly explained.