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If \( \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7}}}}}=7^{x} \), then the value of x |
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Answer» Given : \(\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt7}}}}\) = 7x = 7x = \(\sqrt{7\sqrt{7\sqrt{7\sqrt{7^{3/2}}}}}\) (7√7 = \(\sqrt{7^2\times7}\) = \(\sqrt{7^3}\) = 73/2) = \(\sqrt{7\sqrt{7\sqrt{7\times7^{3/4}}}}\) = \(\sqrt{7\sqrt{7\sqrt{7^{7/4}}}}\) = \(\sqrt{7\sqrt{7\times7^{7/8}}}\) = \(\sqrt{7\times7^{15/16}}\) = 731/32 \(\therefore\) x = \(\cfrac{31}{32}\) |
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