Melody

You can write the 4th root of x either of these ways

$$\\\sqrt[4]{x}\qquad or \qquad x^{1/4}$$

It happened because you did not put \\ after \end{array}

I've done it accidentally before too but I've never experimented to see how it can be useful.

Soon I will be learning off you - I am already starting too!  

No that is because the problems has already been fixed.  

Somehow xvxvxv  who I call 15x3 managed to post a thread without a title and it was difficult to open.

Hi Ninja,

Somehow I think your first solution needs some brackets?  No it still won't work.  Plus you need to swap the 4 for 8/2    

Why don't you try the easier one?  The hard one is REALLY difficult.

Yes okay, thanks Alan.  

Yes but did what I said make sense?  

Actually if you'd presented the integral without anything there I would have been even more confused.  I didn't  know you could have an integral with nothing there.

Thanks Alan,

I can see that a denominator of 5 works for your example but I still don't comprehend where 

$$\int1 dx$$   comes from.  Why is it 1?  What are you finding the sum of?

I obvioulsy have a major gap in my understanding.

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Actually I am just thinking about the units as rates The average of anything can be thought of as whatever per unit or item.  That makes sense. So thinking of it like this I absolutely get the difference on the bottom.

For example (for the benefit of others) The average of 6m,3m and 2m = 9m/3items = 3m/item

So  $$\int1 dx$$  is the sum of units on the x axis which is 5.   

So for the given question the average is     sum of the gradients/unit of x

Does that make sense, sort of anyway?   

Maybe I have got it!  

solution:

I do not know what this notation means.

Do you mean ?

$${{log}}_{{\mathtt{100}}}{\left({\mathtt{0.16}}\right)} = -{\mathtt{0.397\: \!940\: \!008\: \!672\: \!037\: \!6}}$$      

$${{log}}_{{\mathtt{0.16}}}{\left({\mathtt{100}}\right)} = -{\mathtt{2.512\: \!941\: \!594\: \!732\: \!06}}$$

$${log}_{10}\left({\frac{{\mathtt{0.16}}}{{\mathtt{100}}}}\right) = -{\mathtt{2.795\: \!880\: \!017\: \!344\: \!075}}$$

I am sorry, i do not know what you want.