# Inifinity limit with natural log

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1. Sep 27, 2016

### AlexandraMarie112

1. The problem statement, all variables and given/known data
Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3)

2. Relevant equations

3. The attempt at a solution
Ln(x^2-1)/(2x^2+3)

Then I divided the top and bottom by x^2 so in the end I got (1/2).

Is this right?

2. Sep 27, 2016

### LCKurtz

What happened to the $\ln$?

3. Sep 27, 2016

### Mastermind01

Is this what you did? :

$\lim_{n\rightarrow +\infty} {\ln {(x^2 - 1)} - \ln{(2x^2+3)}}$

$= \lim_{n\rightarrow +\infty} {\ln ({\frac{x^2 - 1}{2x^2+3}})}$

$= {\ln {\lim_{n\rightarrow +\infty}(\frac{1 - \frac{1}{x^2}}{2+\frac{3}{x^2}}})}$

You got the limit of the inside part as $\frac{1}{2}$ you need to take its $\ln$ to get the right answer.

4. Sep 27, 2016

### AlexandraMarie112

Yes thats what I did. So my final answer then should be Ln(1/2) ?

5. Sep 27, 2016

### Staff: Mentor

Right, or -ln(2)