cat 2021 Question 2

Question

If $log_{2}$[3 + $log_{3}${4 + $log_{4}$(x - 1)}] - 2 = 0 then 4x equals

Accepted Answer

We have

$\log_2 \{ 3 + \log_3 \{ 4 + \log_4 (x - 1) \} \} = 2$

we get

$3 + \log_3 \{ 4 + \log_4 (x - 1) \} = 4$

we get

$\log_3 (4 + \log_4 (x - 1)) = 1$

we get

$4 + \log_4 (x - 1) = 3$

$\log_4 (x - 1) = -1$

$x - 1 = 4^{-1}$

$x = \frac{1}{4} + 1 = \frac{5}{4}$

4x = 5

Question 2.