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2 comments:
I don't know how to get to the answer. I followed these steps:
Expanded it to ln(x-2)-ln(x-1)=1+ln(x-3)-ln(x-1) and cancelled out the ln(x-1)
brought ln(x-3) from the right side to the left side, making it ln(x-2)-ln(x-3)=1 which becomes ln(x-2/x-3) = 1.
after that i am stuck
You've had good instincts to simplify it like it did. Just as a note, an alternative way to do the same thing:
ln((x-2)/(x-1)) - ln((x-3)/(x-1)) = 1
ln((x-2)*(x-1)/((x-3)*(x-1))) = 1
cancel out then (x-1)'s and then we have
ln((x-2)/(x-3)) = 1
Which is causing the problem.
Some how we have to get the x's outside the ln function. We could do this either by doing something to the left side, which doesn't look possible. OR, you could do something to the right side so that we have
ln((x-2)/(x-3)) = ln(something)
then we could "remove" the ln function, and we'd have
(x-2)/(x-3) = something
so, think about ln(something) = 1.
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