Math Help - Functions involving powers of logarithms

1. Functions involving powers of logarithms

2. You are apparently expected to know the "law of logarithms", $log(a^b)= b log(a)$. Here a= |x| and b= x.

Hi! I quite know the rule you are referring to. The problem is that the two functions do not seem to be the same.
Try and plot them using a calculator. You'll get two different graphs! Thank you for your help anyway.

4. Originally Posted by sanders47
In future please type the question rather than attaching it. The basic latex required for the job is not difficult to learn.

By $\ln^2 |x|^x$ do you mean $(\ln |x|^x)^2$ ? In which case the result given by the book is wrong.

The basic question is what does the book mean and not
what I mean.
I attached my question because:

• I'm a new member and I'm not familiar with latex;
• It was important to show the way the function is written in the book
Thanks.

6. Originally Posted by sanders47
The basic question is what does the book mean and not
what I mean.
I attached my question because:

• I'm a new member and I'm not familiar with latex;
• It was important to show the way the function is written in the book
Thanks.
If you cannot provide the clarification I requested then I don't see how further progress can be made. The meaning I suggested for the notation is a reasonable one, in which case, as I said before, the book is wrong.

8. $\ln^2 |x|^x = (\ln |x|^x)^2 = (x \ln |x|)^2 = x^2 \:\ln^2 |x|$