(b) 9.
log3x + log3 \(\sqrt{x}\) + \(\text{log}_3 (\sqrt[4]x)\) + \(\text{log}_3 (\sqrt[8]x)\)+ ..... \(\infty\) = 4
⇒ log3x + log3x1/2 + log3x1/4 + log3 (x1/8) + ..... ∞ = 4
⇒ log3 (x . x1/2 . x1/4 . x1/8 ..... ∞) = 4
⇒ log3 (x1 + 1/2 + 1/4 + 1/8 ..... ∞) = 4
⇒ log3 \(x^{\frac{1}{1-\frac{1}{2}}}\) = 4 (∞ S∞ = \(\frac{a}{r}\) – r)
⇒ log3 x2 = 4 ⇒ x2 = 34 = (32)2 ⇒ \(x\) = 9.