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how do i solve for x ?

ln x^2 + ln 2x+1 =0 thanks for your help

5 Answers

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  • 1 decade ago
    Favorite Answer

    Remember this natural log rule:

    ln(a x b) = ln a + ln b

    Therefore:

    ln x^2 + ln 2x+1 = 0

    equals:

    ln x^2(2x+1) = 0

    Now take 'e' of both sides:

    e^ln x^2(2x+1) = e^0

    which gives you:

    x^2(2x+1) = 1

    Multiply out the left side. Then move '1' to the left side.

    You get:

    2x^3 + x^2 - 1 = 0

    From here, I used a tweaked version of Cardano's Formula and got this:

    x = 0.5897.

    Hope this helps!

    Source(s): My fault notthejake....got sloppy with my own rules haha. *The tweaked version of Cardano's Formula : http://www.math.vanderbilt.edu/~schectex/courses/c... *
  • 1 decade ago

    remembering that ln a + ln b = ln (ab), this becomes:

    ln(x^2 * (2x + 1)) = 0

    converting to exponential form:

    e^0 = 2x^3 + x^2

    but e^0 = 1, so 2x^3 + x^2 - 1 = 0

    graphically, the only real solution is x = .657

    check:

    ln (.657)^2 = -.8401

    ln(2*.657 + 1) = ln 2.314 = .839

    with rounding errors, -.840 + .839 = 0

    Edit: careful breadcrumbs: e^0 = 1, not 0

  • 1 decade ago

    ln x^2 + ln 2x + 1 = 0

    2 ln x + ln 2 + ln x + 1 = 0

    2 ln x + ln x = -1 - ln 2

    3 ln x = -1 - ln 2

    ln x = (-1 - ln 2) / 3

    x = e^[(-1 - ln 2) / 3]

    x = 0.5687

  • 1 decade ago

    ln x^2 + ln 2x+1=0, or 2lnx+ln2+lnx+1=0, or

    3lnx=-1-ln2=-1.693 or lnx=-.564...or x=.569....done

    check, ln (.569)^2+ln 2(.569)+1=0...or

    -1.128+.1293+1=0...which check out...

    so, ans is x=.569....

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  • 1 decade ago

    i dont know what the in is. but if the problem is x^2+2x+1=0 then all you have to do is simple factoring. so what you need to do here is find what multiples to c, in this case 1 and adds to b, in this case 2.

    1x1=1

    1+1=2

    so the way to factor your problem would be (x+1)(x+1)

    if you want to make sure this is correct, use foil, in other words distribute.

    x times x=x^2

    x times 1=1x

    1 times x=1x

    1x+1x=2X

    1 times 1=1

    once you have your factor, (x+1)(x+1)

    then you would need to set each factors equal to zero. x+1=0

    thus x = -1

    your answer is x equals negative one

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