document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147951>Question 1147951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact solution, using common logarithms. <BR>\n" );
document.write( "log(x − 3) − log(5x − 7) = log(1/x) </SPAN>\n" );
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document.write( "NO!  The two solutions do NOT both work!<br><BR>\n" );
document.write( "The given equation is<br><BR>\n" );
document.write( "(1) log(x − 3) − log(5x − 7) = log(1/x)<br><BR>\n" );
document.write( "To start solving that, you use rules of logarithms:<br><BR>\n" );
document.write( "(2) log((x-3)/(5x-7)) = log(1/x)<br><BR>\n" );
document.write( "Working from there, you find apparent solutions x=1 and x=7.<br><BR>\n" );
document.write( "And those solutions both work in (2).<br><BR>\n" );
document.write( "BUT... they have to satisfy the ORIGINAL equation.  And x=1 does not, because it results in trying to take the logarithm of a negative number.<br><BR>\n" );
document.write( "ANSWER: x=7 is the only solution.<br><BR>\n" );
document.write( " </SPAN>\n" );
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