\(\text{log}_{\sqrt3}\) \(\sqrt{3\sqrt{3\sqrt{3\sqrt{3}}}} =\)(a) \(\

1.	\(\text{log}_{\sqrt3}\) \(\sqrt{3\sqrt{3\sqrt{3\sqrt{3}}}} =\)(a) \(\frac{31}{32}\)(b) \(\frac{15}{16}\)(c) \(\frac{7}{16}\)(d) \(\frac{15}{8}\)
Answer» (d) \(\frac{15}{8}\) Given expression = \(\text{log}_{\sqrt3}\,3^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}\) = \(\text{log}_3{^{\frac{1}{2}}}\) \(3^{\frac{15}{16}}\) = \(\frac{15}{16}\) x 2 log₃ 3 = \(\frac{15}{8}\).

\(\text{log}_{\sqrt3}\) \(\sqrt{3\sqrt{3\sqrt{3\sqrt{3}}}} =\)(a) \(\frac{31}{32}\)(b) \(\frac{15}{16}\)(c) \(\frac{7}{16}\)(d) \(\frac{15}{8}\)

Answer»

(d) \(\frac{15}{8}\)

Given expression = \(\text{log}_{\sqrt3}\,3^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}\)

= \(\text{log}_3{^{\frac{1}{2}}}\) \(3^{\frac{15}{16}}\) = \(\frac{15}{16}\) x 2 log₃ 3 = \(\frac{15}{8}\).