SOLUTION: Can someone please explain how to solve the following 2 problems. Any assistance you can provide is greatly appreciated! the log of (x+5), base 2 + the log of (x-1), base 2 =4 an

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can someone please explain how to solve the following 2 problems. Any assistance you can provide is greatly appreciated! the log of (x+5), base 2 + the log of (x-1), base 2 =4 an      Log On


   

Question 170256: Can someone please explain how to solve the following 2 problems. Any assistance you can provide is greatly appreciated!
the log of (x+5), base 2 + the log of (x-1), base 2 =4
and
the log of 6, base 36 = x
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%5B2%5D%28x%2B5%29+%2B+Log%5B2%5D%28x-1%29+=+4 Apply the "product rule" (Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29+=+Log%5Bb%5D%28M%2AN%29) for logarithms to the left side.
Log%5B2%5D%28%28x%2B5%29%28x-1%29%29+=+4 Simplify the argument on the left side.
Log%5B2%5D%28x%5E2%2B4x-5%29+=+4 Rewrite the left side in its exponential form:(Log%5Bb%5D%28x%29+=+y means b%5Ey+=+x)
2%5E4+=+x%5E2%2B4x-5 Simplify.
x%5E2%2B4x-5+=+16 Subtract 16 from both sides.
x%5E2%2B4x-21+=+0 Factor this quadratic equation.
%28x-3%29%28x%2B7%29+=+0 Apply the zero product rule: If A*B = 0, then either A = 0, or B = 0, or both.
x-3+=+0 or x%2B7+=+0 so that...
x+=+3 or x+=+-7