#### jasongousis72

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x10^x/11^x>=(x+1)10^(x+1)/11^(x+1)

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- Thread starter jasongousis72
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x10^x/11^x>=(x+1)10^(x+1)/11^(x+1)

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So x*x^10/x^11 = x^11/x^11 = 1.

Now (x+1)^10*(x+1) = [(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)]*(x+1) = (x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1)*(x+1) = (x+1)^11

So, (x+1)^10*(x+1)/(x+1)^11 = (x+1)^11/(x+1)^11 =1

For which values of x are both sides equal to one another? Hint: both sides always equal 1.

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Uh- What I see is NOT "x^10" but "10^x"!

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Divide both sides by 10^x to getx10^x/11^x>=(x+1)10^(x+1)/11^(x+1)

x/11^x>= 10(x+1)/11^(x+1)

Multiply both sides by 11^(x+1) to get

11x>= 10(x+ 1)

Distribute the 10 on the right

11x>= 10x+ 10

Subtract 10x from both sides of the equation

x>= 10.