SOLUTION: log (base 7) 2 + log (base 49) x = log (base 1/7) sqrt 3

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Question 921936: log (base 7) 2 + log (base 49) x = log (base 1/7) sqrt 3
Found 2 solutions by mathsnight, MathTherapy:
Answer by mathsnight(4) About Me  (Show Source):
You can put this solution on YOUR website!
Log(base7)2sqrt(3)=log(base7)(x^(-1/2)), then
=> x=1%2F12

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
log (base 7) 2 + log (base 49) x = log (base 1/7) sqrt 3
 log+%287%2C+%282%29%29+%2B+log+%2849%2C+%28x%29%29+=+log+%281%2F7%2C+%28sqrt%283%29%29%29
   
  ---- Converting from base 10 to base 7
  
  
 ---- Multiplying by LCD, 2
  --- Applying a%2Alog+%28b%2C+c%29 = log+%28b%2C+%28c%29%5Ea%29
  log+%287%2C+%284%29%29+%2B+log+%287%2C+%28x%29%29+=+log+%287%2C+%281%2Fsqrt%283%29%29%5E2%29
  log+%287%2C+%284%29%29+%2B+log+%287%2C+%28x%29%29+=+log+%287%2C+%281%2F3%29%29

         log+%287%2C+%284x%29%29+=+log+%287%2C+%281%2F3%29%29 ---- Applying log+%28a%2C+%28b%29%29+%2B+log+%28a%2C+%28c%29%29+=+log+%28a%2C+%28b%2Ac%29%29
               4x+=+1%2F3 ---- Applying b = c, WHEN log+%28a%2C+%28b%29%29+=+log+%28a%2C+%28c%29%29 
              12x = 1 ------ Cross-multiplying
               highlight%28x+=+1%2F12%29