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

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)   (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
---------------------
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)   (Show Source): You can put this solution on YOUR website!

First must definition domain:
X+7>0 and x+3>0 there for domain is x>-3

x^2+10x+21=77
x^2+10x-56=0

that is not acceptable and

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)   (Show Source): You can put this solution on YOUR website!
1n (x+7) + 1n (x+3) = 1n77
------------
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

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