Find x for ln x=-2 using the natural logarithm formula

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SUMMARY

The discussion centers on solving the equation ln x = -2 using the natural logarithm formula. The correct solution is x = e^(-2), which equals approximately 0.135. However, it is emphasized that the natural logarithm function, ln x, is only defined for positive real numbers, making ln(-2) invalid in this context. The conversation clarifies that for negative arguments, a complex logarithm approach is required.

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lnx=-2 ---- find x

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
 
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justin345 said:

Homework Statement



Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
Yes, ln x = -2 <==> x = e-2, which is approximately 0.135.
 


I am asking because for negative natural logs, there is a more complicated formula with sin and cos and Pi.
So you are saying that it is okay to use this one? Thank you!
 


No, I'm not saying that at all. For the real number version of the ln function, the domain is positive real numbers, and the range is all real numbers.

If you had ln(-2), that would be a different matter altogether, and you would need the complex version of this function.
 

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