SOLUTION: how do i solve for x? ln(x+3)-2=ln(x+1)

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Question 4730: how do i solve for x? ln(x+3)-2=ln(x+1)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%2B3%29-2=ln%28x%2B1%29 re-arrange to give ln%28x%2B3%29-ln%28x%2B1%29+=+2. Now, we can use properties of logs to re-write this as:

ln%28%28x%2B3%29%2F%28x%2B1%29%29+=+2. Now we have just 1 log, we can raise everything to the power of e: this is the opposite processes to ln, just like + and - or x and divide are opposites:

%28x%2B3%29%2F%28x%2B1%29+=+e%5E2 --> e is just a number like any other. Do not be scared of it.

%28x%2B3%29+=+%28e%5E2%29%2A%28x%2B1%29
x%2B3+=+xe%5E2+%2B+e%5E2
x-xe%5E2+=+e%5E2-3
x%281-e%5E2%29+=+e%5E2-3

so x+=+%28e%5E2-3%29%2F%281-e%5E2%29

All you have done here is mess around with the order of the equation: manipulated it. Nothing too difficult. Only this you needed to know were a couple of log rules.

You can work this out on a calculator if you need to, but your answer will be an approximation, since you will round up: this algebraic version is the EXACT answer.

jon.