SOLUTION: Log5(7+x)+log5(8-x)-log5(2)=2

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Question 1058225: Log5(7+x)+log5(8-x)-log5(2)=2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert +2+ to a log to the base 5
+log%28+5%2C+7%2Bx+%29+%2B+log%28+5%2C+8-x+%29+-+log%28+5%2C+2+%29+=+2+
+log%28+5%2C+7%2Bx+%29+%2B+log%28+5%2C+8-x+%29+-+log%28+5%2C+2+%29+=+log%28+5%2C+25+%29+
+log%28+5%2C+%28+7%2Bx+%29%2A%28+8+-+x+%29%2F2+%29+=+log%28+5%2C+25+%29+
+%28+7%2Bx+%29%2A%28+8-x+%29%2F2+=+25+
+%28+7%2Bx+%29%2A%28+8-x+%29+=+50+
+56+%2B+8x+-+7x+-+x%5E2+=+50+
+-x%5E2+%2B+x+%2B+6+=+0+
+%28+-x+%2B+3+%29%2A%28+x+%2B+2+%29+=+0+ ( I just figured it out )
+x+=+3+
+x+=+-2+
---------------
check:
I'll check +x+=+-2+
+log%28+5%2C+7%2Bx+%29+%2B+log%28+5%2C+8-x+%29+-+log%28+5%2C+2+%29+=+2+
+log%28+5%2C+7-2+%29+%2B+log%28+5%2C+8%2B2+%29+-+log%28+5%2C+2+%29+=+2+
+log%28+5%2C+5+%29+%2B+log%28+5%2C+10+%29+-+log%28+5%2C+2+%29+=+2+
+1+%2B+log%28+5%2C2+%29+%2B+log%28+5%2C5+%29+-+log%28+5%2C2+%29+=+2+
+1+%2B+1+=+2+
OK
You can check +x=3+