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Alg 2

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Solve the equation. Check for extraneous solutions.

10 ln 100x - 3 = 117

Thank you in advanced

  • Alg 2 - ,

    10 log(100 x)-3 = 117

    Add 3 to both sides:

    10 log(100 x)- 3 = 117 + 3

    10 log(100 x) = 120

    Divide both sides by 10:

    log(100 x) = 12

    Cancel logarithms by taking exp of both sides:

    100 x = e^12

    Divide both sides by 100:

    x = e^12/100

    Now test that this solution is appropriate by substitution into the original equation:

    Check the solution x = e^12/100:

    10 log(100 x)- 3 = -3 + 10 log((100 e^12)/100) = 117

    So the solution is correct.

    Thus, the solution is:

    x = e^12/100

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