the natural log function


by mindheavy
Tags: function, natural
mindheavy
mindheavy is offline
#1
Feb15-13, 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?

Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
mfb
mfb is offline
#2
Feb15-13, 05:02 PM
Mentor
P: 10,813
ln(x^2) = 2 ln(|x|)

As sqrt(x^2)=|x|
mindheavy
mindheavy is offline
#3
Feb15-13, 05:14 PM
P: 61
Ah yes, I had forgotten about that, thank you.

Mark44
Mark44 is offline
#4
Feb15-13, 06:20 PM
Mentor
P: 21,012

the natural log function


The difference in the graphs is entirely due to the domains of the two different functions.

ln(x2) 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.


Register to reply

Related Discussions
Natural Log : seems as a discontinous function General Math 4
Natural exponential Function Calculus & Beyond Homework 2
Differentiation of the natural exponential function (e) Calculus 0
Natural Logarithmic Function Precalculus Mathematics Homework 5
Natural logarithmic function Calculus & Beyond Homework 2