If a^ _b c =3 3^ _4 3 3^ _4 (3^ _4 3 ) 3^ _4 (3^ _4 (3^ _4 3 ) ) to infinity

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

a^{\log_b c}=3\cdot3^{\log_4 3}\cdot3^{\log_4\left(3^{\log_4 3}\right)}\cdot3^{\log_4\left(3^{\log_4\left(3^{\log_4 3}\right)}\right)}\cdots

to infinity, where

a,b,c\in\mathbb{Q}

, then the value of

abc

is (1)

9

(2)

12

(3)

16

(4)

20