SOLUTION: log(x-44)-log7=log(x-14)-logx solve. also this question logx+log(x-3)=1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log(x-44)-log7=log(x-14)-logx solve. also this question logx+log(x-3)=1      Log On


   

Question 686655: log(x-44)-log7=log(x-14)-logx solve.
also this question logx+log(x-3)=1
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

1.
log%28x-44%29-log%287%29=log%28x-14%29-log%28x%29
log%28%28x-44%29%2F7%29=log%28%28x-14%29%2Fx%29
%28x-44%29%2F7=%28x-14%29%2Fx
%28x-44%29%2Ax=%28x-14%29%2A7
x%5E2-44x=7x-98
x%5E2-44x-7x%2B98=0
x%5E2-51x%2B98=0.....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-51%29+%2B-+sqrt%28+%28-51%29%5E2-4%2A1%2A98+%29%29%2F%282%2A1%29+

x+=+%2851+%2B-+sqrt%282601-392+%29%29%2F2+

x+=+%2851+%2B-+sqrt%282209+%29%29%2F2+

x+=+%2851+%2B-+47%29%2F2+
solutions:
x+=+%2851+%2B+47%29%2F2+
x+=+98%2F2+
highlight%28x+=49%29

and

x+=+%2851+-47%29%2F2+
x+=+4%2F2+
highlight%28x+=2%29

2.
log%28x%29%2Blog%28x-3%29=1....we can replace 1 with log%2810%29

log%28x%28x-3%29%29=log%2810%29
x%28x-3%29=10
x%5E2-3x=10
x%5E2-3x-10=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A%28-10%29+%29%29%2F%282%2A1%29+
x+=+%283+%2B-+sqrt%289%2B40%29%29%2F2+
x+=+%283+%2B-+sqrt%2849%29%29%2F2+
x+=+%283+%2B-+7%29%2F2+
solutions:
x+=+%283+%2B+7%29%2F2+
x+=+10%2F2+
highlight%28x+=+5%29+.......for log we use only positive solutions




Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
log(x-44)-log7=log(x-14)-logx solve.

also this question logx+log(x-3)=1
**********************************
This respondent, @MathLover1(20855) did the same thing that @HyperBrain(694) did  for Problem, logarithm/105757. She used the QUADRATIC
EQUATION formula to solve both quadratic equations, which is UNNECESSARY, since the resultant TRINOMIAL is FACTORABLE! Furthermore, the
problem, log(x - 44) - log 7 = log (x - 14) - log (x), has x - 44 as its SMALLEST log variable-argument. This MUST BE > 0, which means that x > 44. 

So, the equation, log(x - 44) - log 7 = log (x - 14) - log (x), will have the following criteria, x > 44.

She got 2 values for x: x = 49, and x = 2. Obviously, 2 is NOT > 44, so x = 2 is an EXTRANEOUS solution, which makes x = 49, VALID/ACCEPTABLE,
and the SOLE SOLUTION.