Question 1139687
{{{ log((log (x))) + log((log (x^4) - 3))) = 0}}}

Assuming "log" is the base {{{10}}}.


 {{{log((log (x)* log (x^4 - 3))) = 0}}}....since {{{0=log(10,1)}}},we have

{{{log((log (x)* (log (x^4) -log( 3)))) = log(10,1)}}}....simplify

{{{log ((x))* 4*log ((x - 3))=1}}}

Rewrite the equation with : {{{log (( x ))=u}}}

{{{u (4u-3 )=1}}}

{{{4u^2-3u=1}}}

{{{4u^2-3u-1=0}}}

{{{4u^2-4u+u-1=0}}}

{{{(4u^2-4u)+(u-1)=0}}}

{{{4u(u-1)+(u-1)=0}}}

{{{(4u+1)(u-1)=0}}}

=>{{{u=1}}} or {{{u=-1/4}}}

then, find {{{log ( 10,x )=u}}}

=> when {{{u=1}}}

{{{log ( 10,x )=1}}}

{{{x=10}}}

=> when {{{u=-1/4}}}

{{{log ( 10,x )=-1/4}}}

{{{x = 10^(-1/4)

{{{x = 1/10^(1/4)}}}

Check the solutions by plugging them into {{{log((log (x))) + log((log (x^4) - 3)) )= 0}}}
{{{log((log (10))) + log((log (10^4) - 3))) = 0}}}........True
{{{ log((log (1/10^(1/4)))) + log((log (1/10^(1/4)) - 3))) = 0}}}.... False
so, your solution is: {{{x=10}}}