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Math Help - Solving an inequality.

  1. #1
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    Solving an inequality.

    problem is solve the inequality:

    2^(2x-1)<3^(3x-2)
    2 to the 2x-1 power<3 to the 3x-2 power

    i have already:

    1) took ln of 2 and 3

    (2x-1)ln2<(3x-2)ln3

    2) factored

    2x*ln(2)-ln(2)<3x*ln(3)-2ln(3)

    3) added ln2 to both sides

    2x*ln(2)<3x*ln(3)+ln(2)-2ln(3)

    I am stuck as to what to do next i know i must isolate the x but dont see how it will work and still be able to come up with the answer provided by a online solver.

    answer is

    x<(ln(2)-2ln(3)) / (2ln(2)-3ln(3))

    please any help would be great!!!!! please if you could explain thank you
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  2. #2
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    Quote Originally Posted by jessmari86 View Post
    problem is solve the inequality:

    2^(2x-1)<3^(3x-2)
    2 to the 2x-1 power<3 to the 3x-2 power

    i have already:

    1) took ln of 2 and 3

    (2x-1)ln2<(3x-2)ln3

    2) factored

    2x*ln(2)-ln(2)<3x*ln(3)-2ln(3)

    3) added ln2 to both sides

    2x*ln(2)<3x*ln(3)+ln(2)-2ln(3)

    I am stuck as to what to do next i know i must isolate the x but dont see how it will work and still be able to come up with the answer provided by a online solver.

    To isolate x, you need x on one side.
    Subtract 3xln3 from both sides, then factor out x next.
    Finally divide both sides by the single remaining multiplier of x

    Archie Meade


    answer is

    x<(ln(2)-2ln(3)) / (2ln(2)-3ln(3))

    please any help would be great!!!!! please if you could explain thank you
    .
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  3. #3
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    2x\ln 2-\ln 2< 3x \ln 2 -2\ln 2

    2x\ln 2< 3x \ln 2 -2\ln 2 +\ln 2

    2x\ln 2- 3x \ln 2< -2\ln 2 +\ln 2

    x(2\ln 2- 3 \ln 2) < -2\ln 2 +\ln 2

    \displaystyle x < \frac{-2\ln 2 +\ln 2}{2\ln 2- 3 \ln 2}

    \displaystyle x < \frac{\ln 2-2\ln 2 }{2\ln 2- 3 \ln 2}
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  4. #4
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    pickslides, the RHS in the question has

    3^{3x-1}

    So when you take ln it will be
    (3x-1)ln3

    So the answer will be

    <br />
x<\frac<br />
{ln2-2ln3}<br />
{2ln2-3ln3}<br />
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