SOLUTION: Find the positive value of x that satisfies the equation Logx-log( x + 6)^1/2 = 0 All the log is in base 2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the positive value of x that satisfies the equation Logx-log( x + 6)^1/2 = 0 All the log is in base 2      Log On


   

Question 1083742: Find the positive value of x that satisfies the equation Logx-log( x + 6)^1/2 = 0
All the log is in base 2
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%282%2C%28x%29%29-log%282%2C%28x+%2B+6%29%5E1%2F2%29+=+0
log%282%2C%28x%29%29-log%282%2Csqrt%28x+%2B+6%29%29+=+0
log%282%2C%28x%29%2Fsqrt%28x+%2B+6%29%29+=+0
log%28%28x%29%2Fsqrt%28x+%2B+6%29%29%2Flog%282%29+=+0
log%28%28x%29%2Fsqrt%28x+%2B+6%29%29+=+0%2Alog%282%29
log%28%28x%29%2Fsqrt%28x+%2B+6%29%29+=+0...........in base 10, log%281%29=0
log%28%28x%29%2Fsqrt%28x+%2B+6%29%29+=+log%281%29.......if log same, we have
x%2Fsqrt%28x+%2B+6%29+=+1
x+=+sqrt%28x+%2B+6%29
x%5E2+=+%28sqrt%28x+%2B+6%29%29%5E2
x%5E2+=+x+%2B+6
x%5E2-x+-+6=0
x%5E2-3x%2B2x+-+6=0
%28x%5E2-3x%29%2B%282x+-+6%29=0
x%28x-3%29%2B2%28x+-+3%29=0
%28x+-+3%29%28x+%2B+2%29+=+0
solutions:
if %28x+-+3%29+=+0->x=3
if %28x+%2B+2%29+=+0->x=-2-> since log, disregard negative solution
so, your solution is x=3


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Logx-log( x + 6)^1/2 = 0
Logx = log( x + 6)^1/2
x = sqrt(x+6)
x^2 - x - 6 = 0
etc