Need some help with these inequalities?

Solved a few, and go to these, which stumped me:

0.5^x<=2^x*1/16

6^x*1/36<(sqrt)6^x

and finally:

(1/9)^x>81*(sqrt)(1/9)^x*1/6561

I'd love to just understand how to solve these.

1 Answer

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  • ?
    Lv 7
    7 years ago
    Best Answer

    xLn(0.5) <= xLn(2)) + Ln(1/16)

    x(Ln(0.5) - Ln(2)) <= Ln(1/16)

    x(-Ln(2) - Ln(2)) <= -4Ln(2)

    -2xLn(2) <= -4Ln(2)

    x => 2

    xLn(6) + Ln(1/36) < xLn(sqrt(6))

    xLn(6) - (1/2)xLn(6) < 2Ln(6)

    (1/2)x < 2

    x < 4

    xLn(1/9) > Ln(81) + xLn(sqrt(1/9)) + Ln(1/6561)

    -2xLn(3) > 4Ln(3) - xLn(3) - 8Ln(3)

    -2x > -4 - x

    x < 4

    And finally (!)

    CFC < MCFC < FCB

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