Solving X with natural logarithm in a fraction

[Jasper20070]

Hi everybody,

I have no clue why this is the answer to this question (see attachment).
Searching the internet have not made me wiser.

Thanks!

 

[Deleted member 4993]

Hi everybody,

I have no clue why this is the answer to this question (see attachment).
Searching the internet have not made me wiser.

Thanks!

Exactly where are you getting lost?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[JeffM]

First, thank you very much for giving us the complete problem that has you stuck.

Second, do you have any difficulty at all in understanding

$$\dfrac{x \ \ln(x + 3)}{x^2 + 1} = 0 \implies x \ \ln(x + 3) = 0.$$
Third, do you have the slightest doubt that

$$x \ \ln(x + 3) = 0 \implies x = 0 \text { or } \ln(x + 3) = 0.$$
If you have a problem in understanding, I suspect it is in one of the next two steps, but how do we know for sure if YOU don’t tell us where you lose the train of reasoning.

 

[Jasper20070]

I'm sorry for not giving enough details.

I don't get the first part xln(x+3)=0. How come you just neglect the denominator.

I can make sense of the second part that xln(x+3)=0 results in x=0 or ln(x-3)=0

And I also get manipulating the equation with e will result in getting rid of the natural logarithm.

Hopefully I gave enough information about my issue with this question.

Thanks!

 

[Steven G]

Can you give us three fractions that equal zero? Then we will go further.

 

[JeffM]

I'm sorry for not giving enough details.

I don't get the first part xln(x+3)=0. How come you just neglect the denominator.

I can make sense of the second part that xln(x+3)=0 results in x=0 or ln(x-3)=0

And I also get manipulating the equation with e will result in getting rid of the natural logarithm.

Hopefully I gave enough information about my issue with this question.

Thanks!

$$\dfrac{a}{b} = 0 \implies b \ne 0 \text { and } a = 0.$$
If a fraction is determinate and equals zero, then the denominator numerator equals zero. ...............................edited

This is a mathematical result that is useful in calculus fairly often.