SOLUTION: I need help solving the problem----------- ----> ln x+ ln(x-2)=1

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Question 22615: I need help solving the problem----------------> ln x+ ln(x-2)=1
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
USE FORMULA LOG X + LOG Y =LOG X*Y
YOU USED LN WHICH IS NORMALLY USED FOR LOGARITHMS WITH BASE E,WHERE AS LOG IS USED TO INDICATE BASE 10.I THINK THE PROBLEM IS FOR BASE 10 AND NOT E.SO I AM USING LOG TO SHOW BASE 10 INSTEAD OF LN .ANY WAY IF IT IS REALLY TO BASE N ,THEN ANSWER WILL CHANGE AS SHOWN BELOW
LOG X +LOG (X-2)=LOG X*(X-2)=1=LOG 10(TO BASE 10,WE GET 1=LOG 10 SINCE 10^1=10....IF IT IS BASE E WE GET 1=LOG E)
TAKING ANTILOGS
X(X-2)=10 .......OR E
X^2-2X-10=0
USING QUADRATIC EQN.FORMULA
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ,WE HAVE A=1,B=-2,C=-10
x+=+%282+%2B-+sqrt%28+4%2B40%29%29%2F%282%29+
X=%281+%2B-sqrt%2811%29%29...IF IT IS BASE E , THE ANSWER WOULD BE
X=%281%2B-sqrt%281%2BE%29%29