Logarithm!

Algebra Level 2

If l o g 2 [ − 1 + x 2 − 14 x + 49 ] = 4 log_{2} [-1 + \sqrt{x^{2}-14x+49}] = 4 Then the sum of the values of x is equal to


The answer is 14.

Rayyan Shahid by Rayyan Shahid , 20, India

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2 solutions

Kapil Chandak
Oct 28, 2014

It means 16=-1+(x^2-14x+49)^1/2. So,289=x^2-14x+49. So,x^2-14x-240=0. And the addition of the roots of this quadratic equation is (-b/a)=-(-14)/1=14

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Aarabdh Tiwari
Dec 27, 2014

This is simplified as -1+।x-7।=16 So two solutions as 1. -1+x-7=16 => x=24 2. -1+7-x=16 => x=-10

Sum=> 24-10= 14

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Simplified for youngers

Aarabdh Tiwari - 6 years, 5 months ago

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