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Question 13: 4^{6+12+18+24+…+6x} = (0.0625)^{-84}, what is the value of x?

- 7
- 6
- 9
- 12

7

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Take right side expression,

(0.0625)^{-84 } = \\frac{1}{16}\\)^{-84 }

= (4^{-2})^{-84}

= 4^{168}

Take left side expression

4^{6+12+18+24+…+6x} = 4^{6(1+2+3+4+x)}

= 4^{6} * 4^{(1+2+3+4+…+x)}

= 4^{6} * 4^{x(x+1)/2} (using the formula for sum of natural numbers from 1 to x)

Equating left and right side expresssions, we get 4^{6} * 4^{x(x+1)/2} = 4^{168}

Or 4^{6} * 4^{x(x+1)/2} = 4^{6*28}

=> \\frac{x(x+1)}{2}\\) = 28

or x (x + 1) = 56

Solving for x we get, x = 7

The question is **"what is the value of x?"**

Choice A is the correct answer.

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