# 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

Relevance

- ?Lv 77 years agoBest 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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