SOLUTION: log of (x-6) in base 11 plus the log of (x-4) in base 11 equals 1. I am having a lot of trouble with this please help

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Question 617482: log of (x-6) in base 11 plus the log of (x-4) in base 11 equals 1. I am having a lot of trouble with this please help
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%2811%2Cx-6%29+%2B+log%2811%2Cx-4%29+=+1+
Use the general rule:
+log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+
+log%2811%2Cx-6%29+%2B+log%2811%2Cx-4%29+=+log%2811%2C%28x-6%29%2A%28x-4%29%29+
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In the inverse notation, what this tells me is:
+11%5E1+=+%28x-6%29%2A%28x-4%29+
+x%5E2+-+10x+%2B+24+=+11+
+x%5E2+-+10x+%2B+13+=+0+
Use the quadratic formula to solve:
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-10+
+c+=+13+
+x+=+%28+-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2+-+4%2A1%2A13+%29%29+%2F+%282%2A1%29+
+x+=+%28+10+%2B-+sqrt%28+100+-+52+%29%29+%2F+2+
+x+=+%28+10+%2B-+sqrt%28+48+%29%29+%2F+2+
+x+=++5+%2B-+2%2Asqrt%283%29+
check:
+log%2811%2C5+%2B+2%2Asqrt%283%29+-+6%29+%2B+log%2811%2C5+%2B+2%2Asqrt%283%29+-+4%29+=+1+
+log%2811%2C2%2Asqrt%283%29+-+1%29+%2B+log%2811%2C2sqrt%283%29+%2B+1%29+=+1+
+log%2811%2C+%282%2Asqrt%283%29+-+1%29%2A%282%2Asqrt%283%29+%2B+1%29%29+=+1+
+log%2811%2C12+-+1%29+=+1+
+log%2811%2C11%29+=+1+