Question

14. log[logbase3(logbase4 x)] = 1
​

Answer 1

$log_{}( log_{3}( log_{4}(x) ) ) = log_{1}(1) \\ log_{3}( log_{4}(x) ) = 1 \\ log_{3}( log_{4}(x) ) = log_{3}(3) \\ log_{4}(x) = 3 \\ log_{4}(x) = 3log_{4}(4) \\ x = {4}^{3} \\ x = 64$

Answer 2

$\large{ \bold{ log \: log_{3} \: log_{4} \: x = 1}} \\ \\ = > \large{ \bold{raising \: the \: term \: on \: lhs \: and \: rhs \: to \: the \: power \: e}} \\ \\ = > \large{ \bold{ {e}^{ log log_{3} log_{4}x } = {e}^{1} }} \\ \\ = > \large{ \bold{ log_{3} log_{4}x = e }} \\ \\ \large{ \bold{now \: raising \: the \: terms \: to \: the \: power \: 3}} \\ \\ = > \large{ \bold{ {3}^{ log_{3} log_{4}x } = {3}^{e} }} \\ \\ = >\large{ \bold{ log_{4}x = {3}^{e} }} \\ \\ \large{ \bold{raising \: the \: terms \: to \: the \: power \: 4}} \\ \\ = > \large{ \bold{ {4}^{ log_{4}x} = {4}^{ {3}^{e} } }} \\ \\ = > \large{ \bold{x = {4}^{ {3}^{e} } }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \color{violet}{ \boxed{\large{ \bold{\mathfrak{ \: therefore \: x \: = {4}^{ {3}^{e} } }}}}}$

$\color{blue}{ \large{ \bold{Hope {}^{ \infty } \: it \: Helps {}^{ \infty } }}}$