SOLUTION: I need help solving this problem: 1n (x+7) + 1n (x+3) = 1n77

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Question 446792: I need help solving this problem:
1n (x+7) + 1n (x+3) = 1n77
Found 3 solutions by chriswen, mohammadrezai, Alan3354:
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
1n (x+7) + 1n (x+3) = 1n77
ln x + ln 7 + ln x + ln 3 = ln 77 ****** Problem here
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2 ln x + ln 7*3 = ln77
2 ln x = ln 77 - ln 21
ln x^2 = ln 77/21
x^2 = 77/21
x = sqrt (77/21)
x = 1.915
x must be positive as you can't have negative ln.

Answer by mohammadrezai(14) About Me  (Show Source):
You can put this solution on YOUR website!
1n+%28x%2B7%29+%2B+1n+%28x%2B3%29+=+1n+77
First must definition domain:
X+7>0 and x+3>0 there for domain is x>-3
1n+%28x%2B7%29+%2B+1n+%28x%2B3+%29+=+ln+%28x%5E2%2B10x%2B21%29=+ln+77
x^2+10x+21=77
x^2+10x-56=0
x+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-56%29+%29%29%2F%282%2A1%29+
x1+=+%28-10+-+sqrt%28+324+%29%29%2F+2+
x1=+%28-10-18%29%2F2=-14 that is not acceptable and
x2+=+%28-10+%2B+sqrt%28324%29%29%2F+2+
x2=%28-10%2B18%29%2F2=4 is acceptable and is answer.
Other solution is
ln a ln b= ln 77 find a and b that multiple are 77.
a=7 and b= 11 (or a=11 and b=7)! There for x=4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1n (x+7) + 1n (x+3) = 1n77
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It's LN, not 1n, means natural log.
(x+7) * (x+3) = 77
Check for integer solution.
77 has only 2 factors, 7 and 11
x+7 = 11
x+3 = 7
--> x = 4