SOLUTION: {{{ln(x)-ln(x-3)=1}}}

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Question 605698: ln%28x%29-ln%28x-3%29=1
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
We can use the rule for log/ln that says that the difference of two lns is the ln of the two divided into each other:
ln%28x%29-ln%28x-3%29=1
ln%28x%2F%28x-3%29%29=1
Now, we need to get rid of the ln, just as we would raise everything to base 10 if we were trying to get rid of log, when using ln we will use e instead. Leaving:
%28x%2F%28x-3%29%29=e%5E1
Now, we just need to solve for x, so we can multiply out the denominator:
x=e%5E1%28x-3%29
x=e%5E1x-3e%5E1
x-e%5E1x=-3e%5E1
x%281-e%5E1%29=-3e%5E1
x=%28-3e%5E1%29%2F%281-e%5E1%29
(Note that we can use our calculators to get a decimal value for this, though this answer is still perfectly correct as well, assuming I didn't make a silly error ;) --- if you are unsure about any of the steps taken please let me know and I can help further:) )