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Math Help - Help with solving exponential/log equations

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    44

    Help with solving exponential/log equations

    Can you please help me with the following.

    Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

    7^x=6^(x+7)




    Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

    log10 (x-30)= 3 - log10 x
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  2. #2
    Member
    Joined
    Oct 2007
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    On the top, use the power rule (see other post I answered).

    x ln 7 = x + 7 ln 6

    That is a messy equation.

    Divide each side by (x + 7).

    \frac {x ln 7}{x + 7}
    According to a logarithmic rule (whose name alludes me),
    \frac {ln 7}{7} .

    Then solve with your calculator with decimal place for 2 places.

    That "logarithmic rule" probably doesn't exist so you better wait for another answer.

    For the second problem,
    Remember that log 10 = 1.
    The solve.
    I don't know what it means by
    Be sure to reject any value that is not in the domain of the original logarithmic expressions.

    "Give an exact answer."
    means dont give a decimal because it's probably a fraction or square root.
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