document.write( "Question 311717: log(2x-3)+ log(x-2)=2logx
\n" ); document.write( "Please solve for x and show the work thank you \n" ); document.write( "
Algebra.Com's Answer #222968 by ankor@dixie-net.com(22740)\"\" \"About 
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log(2x-3)+ log(x-2) = 2log(x)
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\n" ); document.write( "log((2x-3)*(x-2)) = log(x^2)
\n" ); document.write( "FOIL
\n" ); document.write( "log(2x^2-4x-3x+6) = log(x^2)
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\n" ); document.write( "log(2x^2 - 7x + 6) = log(x^2)
\n" ); document.write( "therefore
\n" ); document.write( "2x^2 - 7x + 6 = x^2
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\n" ); document.write( "2x^2 - x^2 - 7x + 6 = 0
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\n" ); document.write( "x^2 - 7x + 6 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(x - 6)(x - 1) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 6
\n" ); document.write( "and
\n" ); document.write( "x = 1
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\n" ); document.write( ":
\n" ); document.write( "Check both solutions in original problem
\n" ); document.write( "log(2x-3)+ log(x-2) = 2log(x)
\n" ); document.write( "x=6
\n" ); document.write( "log(2(6)-3)+ log(6-2) = 2log(6)
\n" ); document.write( "log(9) + log(4) = log(6^2)
\n" ); document.write( "log(36) = log(36)
\n" ); document.write( "x = 6; a good solution
\n" ); document.write( ":
\n" ); document.write( "x=1, not a solution, the log of a negative number not permitted
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