CAT 2021 Slot 2 QA Question 8: If $\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] - 2 = 0$ then $4x$ equals

Question

If $\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] - 2 = 0$ then $4x$ equals

Accepted Answer

Move step by step from the outer logarithm to the inner logarithm.

$\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] = 2$
$3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} = 4$
$\log_3 \left\{ 4 + \log_4 (x-1) \right\} = 1$
$4 + \log_4 (x-1) = 3$
$\log_4 (x-1) = -1$
$x-1=4^{-1}=\dfra

If log⁡2[3+log⁡3{4+log⁡4(x−1)}]−2=0\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] - 2 = 0log2​[3+log3​{4+log4​(x−1)}]−2=0 then 4x4x4x equals

If $\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] - 2 = 0$ then $4x$ equals