## help me solve: log (x + 3) - log (x - 1) = log 2

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
milynx
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### help me solve: log (x + 3) - log (x - 1) = log 2

please help me solve this logaritm. Log (x + 3) - log (x - 1) = log 2

stapel_eliz
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Log (x + 3) - log (x - 1) = log 2
To start in solving this log equation, first apply a log rule to convert the left-hand side to one log containing a rational expression.

. . . . .$\log\left(\frac{x\, +\, 3}{x\, -\, 1}\right)\, =\, \log(2)$

At which point, you have "log(something) = log(2)". Set "something" equal to 2, and solve the resulting rational equation.

milynx
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Joined: Mon Jul 27, 2009 9:46 pm
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### Re: help me solve: log (x + 3) - log (x - 1) = log 2

thank you. I ended up with x = 5. hope this is correct. thanks again!

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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You can check the answer to any "solving" exercise by plugging it back into the original problem. In your case:

. . . . .$\log\left(\frac{5\, +\, 3}{5\, -\, 1}\right)\, =\, \log\left(\frac{8}{4}\right)\, =\, \log(2)$

Since your solution "checks", it must be correct!

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