Question

Solve for x:-
log(log x) + log(log x³-2)=0, where base of log is 10 everywhere.

Answer 1

given
   Log (log x)  +  Log ( Log x³  - 2 ) = 0
       =>  Log  [  (log x) (3 Log x - 2) ]  =  0
       =>   (Log x )  * (3 Log x - 2) = 1

     As we have Log (log x) defined,  log x is positive.

Let Log x = z,         So we have

          z * (3 z - 2) = 1
          3 z² - 2 z - 1 = 0
           The factors of  3*-1 are  -3 and +1, and their sum is -2.
           (3z + 1) (z - 1)  = 0

  So   z = -1/3   or   z = 1.      we ignore the negative value, for the reason mentioned above.
  So    Log x = 1
   =>    x =   10.

Answer 2

Answer:

Please Refer to the attachment.