1.

If \( \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7}}}}}=7^{x} \), then the value of x

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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