Calculus

Solve for x log(base6)(x+3)−log(base6)(x−5)=2.

I tried to factor out the log(base6) and got (x+3)^x/(x-5)=2, but I don't know how to solve that...

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asked by Ann
  1. sorry it's log(base6)(x+3)−log(base6)(x−5)=2

    the x in front of log isn't part of it

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    posted by Ann
  2. Oh no, 6 is not a number, it is an operator.

    You can't factor out 6
    (that would be doing something like
    √8 - √3
    = (√)(8-3) )

    You have to use your rules of logs.

    6(x+3) - 6(x-5) = 2
    6 ( (x+3)/(x-5) ) = 2

    which by definition is
    (x+3)/(x-5) = 6^2 = 36
    36x - 180 = x+3
    35x = 183
    x = 183/35

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    posted by Reiny
  3. Oh no, log6 is not a number, it is an operator.

    You can't factor out log6
    (that would be doing something like
    √8 - √3
    = (√)(8-3) )

    You have to use your rules of logs.

    log6(x+3) - log6(x-5) = 2
    log6 ( (x+3)/(x-5) ) = 2

    which by definition is
    (x+3)/(x-5) = 6^2 = 36
    36x - 180 = x+3
    35x = 183
    x = 183/35

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    posted by Reiny
  4. thank you for your explanation :)

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    posted by Ann

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