SOLUTION: Solve for x: {{{ log(8,(log(4,(log(2,x) ) ))) }}}={{{0}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x: {{{ log(8,(log(4,(log(2,x) ) ))) }}}={{{0}}}      Log On


   

Question 113802: Solve for x:
+log%288%2C%28log%284%2C%28log%282%2Cx%29+%29+%29%29%29+=0
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log(base8)(log(base4)(log(base2)x))=0
log(base4)(log(base2)x)) = 8*0=1
log(base2)x = 4^1 = 4
x = 2^4 = 16
===============
Cheers,
Stan H.

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

+log%288%2C%28log%284%2C%28log%282%2Cx%29+%29+%29%29%29+=0
    
Using the rule b%5Elog%28b%2CA%29 = A,
raise 8 to the left side power and set
that equal to 8 raised to the right
side power:

+log%288%2C%28log%284%2C%28log%282%2Cx%29+%29+%29%29%29+=0 

8%5E+log%288%2C%28log%284%2C%28log%282%2Cx%29+%29+%29%29%29+ = 8%5E0

Simplify using the rule above

log%284%2C%28log%282%2Cx%29++%29%29+ = 1

Remembering that same rule again,
raise 4 to the left side power and set
that equal to 4 raised to the right
side power: 

4%5Elog%284%2C%28log%282%2Cx%29++%29%29+ = 4%5E1
  
Using that rule, raise 4 to the left side 
power and set that equal to 4 raised to 
the right side power: 

Simplify using the same rule:

log%282%2Cx%29+++ = 4

Remembering that same rule one final time,
raise 2 to the left side power and set
that equal to 2 raised to the right
side power:

2%5Elog%282%2Cx%29+++ = 2%5E4

Simplify using the same rule:

x = 16

Edwin