document.write( "Question 685646: how do you solve the logarithmic equation log9(x-6)+log9(x-6)=1 \n" ); document.write( "

Algebra.Com's Answer #424517 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The trick is to make the substitution:
\n" ); document.write( " $\"+1+=+log%28+9%2C9+%29+\"$
\n" ); document.write( " $\"++log%289%2C%28x-6%29%29+%2B+log%289%2C%28x-6%29%29+=+1+\"$
\n" ); document.write( " $\"++log%289%2C%28x-6%29%29+%2B+log%289%2C%28x-6%29%29+=+log%28+9%2C9+%29+\"$
\n" ); document.write( " $\"++log%289%2C%28x-6%29%5E2%29+=+log%28+9%2C9+%29+\"$
\n" ); document.write( " $\"+%28+x-6+%29%5E2+=+9+\"$
\n" ); document.write( " $\"+x%5E2+-+12x+%2B+36+=+9+\"$
\n" ); document.write( " $\"+x%5E2+-+12x+%2B+27+=+0+\"$
\n" ); document.write( " $\"+%28+x+-+3+%29%2A%28+x+-+9+%29+=+0+\"$
\n" ); document.write( " $\"+x+=+3+\"$
\n" ); document.write( " $\"+x+=+9+\"$
\n" ); document.write( "---------
\n" ); document.write( "Only $\"+x=9+\"$ is valid. If you plug in
\n" ); document.write( " $\"+x+=+3+\"$ , then
\n" ); document.write( " $\"++log%289%2C%283-6%29%29+%2B+log%289%2C%283-6%29%29+=+1+\"$
\n" ); document.write( " $\"++log%289%2C+%28-3%29%29+%2B+log%289%2C+%28-3%29%29+=+1+\"$
\n" ); document.write( "You can't have a log to a positive base
\n" ); document.write( "that gives you a negative number\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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