Question

plz solve 51. Ans. is (3) 31/32 but plz tell how it comes

Answer 1

Hey here is your answer
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$\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } = {7}^{x} \\ \\ {7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } = {7}^{2x} \\ \\ \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } = {7}^{2x - 1} \\ \\ 7 \sqrt{7 \sqrt{7 \sqrt{7} } } = { {7}^{(2x - 1)} }^{2} \\ \\ \sqrt{7 \sqrt{7 \sqrt{7} } } = { {7}^{(4x - 2 - 1)} } \\ \\ 7 \sqrt{7 \sqrt{7} } = {{ {7}^{(4x - 3)} }}^{2} \\ \\ \sqrt{7 \sqrt{7} } = {7}^{(8x - 6 - 1)} \\ \\ 7 \sqrt{7} = {{7}^{(8x - 7)}}^{2} \\ \\ \sqrt{7} = {7}^{(16x - 14 - 1)} \\ \\ 7 = {{7}^{(16x - 15)}}^{2} \\ \\ {7}^{1} = {7}^{(32x - 30)} \\ \\ 1 = 32x - 30 \\ \\ 30 + 1 = 32x \\ \\ \frac{31}{32} = x \\ \\ x = \frac{31}{32}$
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@ajaman
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