Question

solve this question with detailed explanation plz​

Answer 1

Answer:

$\boxed{\pink{\huge{3}}}$

Step-by-step explanation:

$\bold{Given}\longrightarrow \\ log_{4}(2 log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) ) = \dfrac{1}{2}$

$\bold{To \: find}\longrightarrow \\ value \: of \: x$

$\bold{Concept}\longrightarrow \: used \\ if \\ log_{m}(x) = n \\ = > x = {m}^{n}$

$\bold{Solution}\longrightarrow \\ log_{4}(2 log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) ) = \dfrac{1}{2} \\ = > 2 log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) = {(4)}^{ \frac{1}{2} }$

$= > 2 log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) = { ({2}^{2}) }^{ \frac{1}{2} }$

$= > 2 log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) = 2 \\ 2 \: is \: cancel \: out \: from \: both \: sides$

$= > log_{3}(1 + log_{2}(1 + 3 log_{3}(x) ) ) = 1$

$= > 1 + log_{2}(1 + 3 log_{3}(x) ) = {3}^{1}$

$= > log_{2}(1 + 3 log_{3}(x) ) = 3 - 1$

$= > log_{2}(1 + 3 log_{3}(x) ) = 2$

$= > 1 + 3 log_{3}(x) = {2}^{2}$

$= > 3 log_{3}(x) = 4 - 1$

$= > 3 log_{3}(x) = 3$

$= > log_{3}(x) = 1$

$= > x = {3}^{1}$

$= > x = 3$