What is $lim_(xrarroo)(ln(6x+10)-ln(7+3x))$ ?

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Answer 1 · 2015-10-31T15:22:37

I found: $ln2$

Using a property of logs we can write:

$lim_(x->oo)[ln(6x+10)-ln(7+3x)]=$

$=lim_(x->oo)[ln((6x+10)/(7+3x))]=$

collect $x$ :

$=lim_(x->oo)[ln((cancel(x)(6+10/x))/(cancel(x)(7/x+3)))]=$

as $x->oo$ then $a/x->0$ so:

$=lim_(x->oo)[ln(((6+10/x))/((7/x+3)))]=ln(6/3)=ln2$

What is lim_(xrarroo)(ln(6x+10)-ln(7+3x))lim_(xrarroo)(ln(6x+10)-ln(7+3x))?