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Math Help - Log Equations

  1. #1
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    Log Equations

    Solve each log equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

    (1) -2 log_4 (x) = log_4 (9)

    (2) ln (x + 1) - ln x = 2

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  2. #2
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    Quote Originally Posted by magentarita View Post
    Solve each log equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

    (1) -2 log_4 (x) = log_4 (9)

    (2) ln (x + 1) - ln x = 2
    1.)
    -2 \log _4 (x) = \log_4 (9)
    A general rule is: a \log (x) = \log (x^a)
    Hence: \log_4(x^{-2}) = \log_4(9)
    \log_4\left(\frac{1}{x^2}\right) = \log_4(9)
    As both sides are to the same logarithm base, we can equate the changing variable hence:
    \frac{1}{x^2} = 9
    Now solve for x


    2.)
    \ln (x+1) - \ln x = 2
    A general rule is: \ln (a) - \ln (b) = \ln \left(\frac{a}{b}\right)
    Hence: \ln \left(\frac{x+1}{x}\right) = 2
    A general rule is: e^{\ln(ax)} = ax
    Hence: e^{\ln \left(\frac{x+1}{x}\right)} = e^{2}
    \frac{x+1}{x} = e^{2}
    Now solve for x using algebra skills.
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  3. #3
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    Air...

    Great reply as always. Where have you been, Air?
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