SOLUTION: Find {{{ x^(-1/2) }}}, if {{{ log(7,(log(3,(log(2,x))))) = 0}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find {{{ x^(-1/2) }}}, if {{{ log(7,(log(3,(log(2,x))))) = 0}}}      Log On


   

Question 1112173: Find +x%5E%28-1%2F2%29+, if +log%287%2C%28log%283%2C%28log%282%2Cx%29%29%29%29%29+=+0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Work backwards and simplify,
log%287%2C%28y%29%29=0
y=1
.
.
.
log%283%2C%28z%29%29=1
.
.
.
z=3
.
.
.
log%282%2C%28x%29%29=3
x=8
So then,
8%5E%28-1%2F2%29=1%2Fsqrt%288%29
8%5E%28-1%2F2%29=sqrt%282%29%2F4