document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #388357 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
\"+log%2811%2Cx-6%29+%2B+log%2811%2Cx-4%29+=+1+\"
\n" ); document.write( "Use the general rule:
\n" ); document.write( "\"+log%28a%29+%2B+log%28b%29+=+log%28a%2Ab%29+\"
\n" ); document.write( "\"+log%2811%2Cx-6%29+%2B+log%2811%2Cx-4%29+=+log%2811%2C%28x-6%29%2A%28x-4%29%29+\"
\n" ); document.write( "---------------
\n" ); document.write( "In the inverse notation, what this tells me is:
\n" ); document.write( "\"+11%5E1+=+%28x-6%29%2A%28x-4%29+\"
\n" ); document.write( "\"+x%5E2+-+10x+%2B+24+=+11+\"
\n" ); document.write( "\"+x%5E2+-+10x+%2B+13+=+0+\"
\n" ); document.write( "Use the quadratic formula to solve:
\n" ); document.write( "\"+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"
\n" ); document.write( "\"+a+=+1+\"
\n" ); document.write( "\"+b+=+-10+\"
\n" ); document.write( "\"+c+=+13+\"
\n" ); document.write( "\"+x+=+%28+-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2+-+4%2A1%2A13+%29%29+%2F+%282%2A1%29+\"
\n" ); document.write( "\"+x+=+%28+10+%2B-+sqrt%28+100+-+52+%29%29+%2F+2+\"
\n" ); document.write( "\"+x+=+%28+10+%2B-+sqrt%28+48+%29%29+%2F+2+\"
\n" ); document.write( "\"+x+=++5+%2B-+2%2Asqrt%283%29+\"
\n" ); document.write( "check:
\n" ); document.write( "\"+log%2811%2C5+%2B+2%2Asqrt%283%29+-+6%29+%2B+log%2811%2C5+%2B+2%2Asqrt%283%29+-+4%29+=+1+\"
\n" ); document.write( "\"+log%2811%2C2%2Asqrt%283%29+-+1%29+%2B+log%2811%2C2sqrt%283%29+%2B+1%29+=+1+\"
\n" ); document.write( "\"+log%2811%2C+%282%2Asqrt%283%29+-+1%29%2A%282%2Asqrt%283%29+%2B+1%29%29+=+1+\"
\n" ); document.write( "\"+log%2811%2C12+-+1%29+=+1+\"
\n" ); document.write( "\"+log%2811%2C11%29+=+1+\"\r
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