CAT 2021 Slot 2 · Quant · Question 2

Peel the logarithms off one layer at a time, from the outside in.

{\log}_{2}\left[ \,\cdot \, \right]=2, so the bracket equals {2}^{2}=4

3+{\log}_{3}\{4+{\log}_{4}\left( x-1 \right)\}=4, giving {\log}_{3}\{\,\cdot \,\}=1.

So the brace equals

{3}^{1}=3

4+{\log}_{4}\left( x-1 \right)=3, giving {\log}_{4}\left( x-1 \right)=-1.

Hence x-1={4}^{-1}=\frac{1}{4},

so x=\frac{5}{4} and 4x=5.