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Math Help - Can someone help me solve this logarithmic equation?

  1. #1
    s3a
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    Can someone help me solve this logarithmic equation?

    Can someone help me solve the attached logarithmic equation?
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  2. #2
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    e^(i*pi)'s Avatar
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    Rewrite 3 as log_2(8)

    log_2(x+3) + log_2(x-4) - log_2(8) = 0

    Using the laws of logs combine into one log

    log_2(\frac{(x+3)(x-4)}{8}) = 0

    Remove the log:

    \frac{(x+3)(x-4)}{8} = 1

    and solve
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  3. #3
    s3a
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    I get x = 5 and x = -4 but the solution guide rejects the x = -4. Is this because plugging in the value of -4 into the logarithmic expression is not possible or as the calculator would "error?"
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by s3a View Post
    I get x = 5 and x = -4 but the solution guide rejects the x = -4. Is this because plugging in the value of -4 into the logarithmic expression is not possible or as the calculator would "error?"
    -4 is rejected because there are no real solutions to a negative logarithm. Since all logs must be greater than 0 only x=5 is a solution
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