Question 57

If $$\sqrt{7\sqrt{7\sqrt{7\sqrt{7....}}}} = (343)^{y - 1}$$, then y is equal to

Solution

$$ \sqrt{7\sqrt{7\sqrt{7\sqrt{7....}}}} = x $$

$$ x = \sqrt{7}x $$

$$ x^2 = 7x $$

$$ x^2 - 7x = 0 $$

x=0,7

neglect 0 x = 7

now $$ 7 = (343)^{y-1} $$

$$ (343)^{\frac{1}{3}} = (343)^{y-1} $$

$$ \frac{1}{3} = y - 1 $$

$$ y = \frac{4}{3} $$

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