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The natural log function 
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#1
Feb1513, 04:39 PM

P: 61

I'm reading back over a calculus book getting ready for an exam and I'm seeing a note that I don't understand.
It says to make sure, when rewriting a ln function that the domain is the same, then it provides an example of when it's not the same, yet says nothing more. Is this rewritten form valid? 


#2
Feb1513, 05:02 PM

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P: 11,576

ln(x^2) = 2 ln(x)
As sqrt(x^2)=x 


#3
Feb1513, 05:14 PM

P: 61

Ah yes, I had forgotten about that, thank you.



#4
Feb1513, 06:20 PM

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P: 21,216

The natural log function
The difference in the graphs is entirely due to the domains of the two different functions.
ln(x^{2}) is defined for all real x ≠ 0. 2 ln(x) is defined only for x > 0. The rules for logarithms contain limitations on the values of the arguments. For example, ln(a*b) = ln(a) + ln(b), where a > 0 and b > 0. Note that it is possible for ln(a * b) to be defined even though the right side is undefined. This can happen when both a and b are negative. 


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