SOLUTION: This equation is on a work sheet that I need to solve: log2 (5X+7) - log2 (X) = 2 (note : log2 is log base 2, I can't make subscripts) Please help!!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: This equation is on a work sheet that I need to solve: log2 (5X+7) - log2 (X) = 2 (note : log2 is log base 2, I can't make subscripts) Please help!!      Log On


   

Question 70985: This equation is on a work sheet that I need to solve:
log2 (5X+7) - log2 (X) = 2
(note : log2 is log base 2, I can't make subscripts)
Please help!!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this!
Apply the qoutient rule for logarithms:Log%28M%29-Log%28N%29+=+Log%28M%2FN%29
Log%5B2%5D%285x%2B7%29-Log%5B2%5D%28x%29+=+Log%5B2%5D%28%285x%2B7%29%2Fx%29, so now you have:
Log%5B2%5D%28%285x%2B7%29%2Fx%29+=+2 Rewrite this in exponential form:
2%5E2+=+%285x%2B7%29%2Fx
4+=+%285x%2B7%29%2Fx Multiply both sides by x.
4x+=+5x%2B7 Subtract 5x from both sides.
-x+=+7 Multiply both sides by -1.
x+=+-7
Check:
Log%5B2%5D%28%285x%2B7%29%2Fx%29+=+2 Substitute x = -7.
Log%5B2%5D%28%28%285%28-7%29%2B7%29%29%2F%28-7%29%29+=+2 Simplify.
Log%5B2%5D%28-28%2F-7%29+=+2
Log%5B2%5D%284%29+=+2 Change the base from 2 to 10.
Log%5B2%5D%284%29+=+%28Log%5B10%5D%284%29%29%2FLog%5B10%5D%282%29 Evaluate using your calculator or log tables.
%28Log%5B10%5D%284%29%29%2F%28Log%5B10%5D%282%29%29+=+2