document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542445>Question 542445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question states: Solve each logarithmic equation\r<BR>\n" );
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document.write( "1.) log(3x-1)=log(x-3)+log6\r<BR>\n" );
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document.write( "How do i solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354575 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic logarithm concepts used to solve this problem are:\r<BR>\n" );
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document.write( "log(a) + log(b) = log(a*b)<BR>\n" );
document.write( "log(a) - lob(b) = log(a/b)<BR>\n" );
document.write( "log(a) = b if and only if 10^b = a\r<BR>\n" );
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document.write( "note that log(a) means log(a) to the base of 10.<BR>\n" );
document.write( "if the base is 10, then it doesn't have to be shown.<BR>\n" );
document.write( "if the base is anything other than 10, then it has to be shown.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "log(5,a) means log of a to the base of 5.\r<BR>\n" );
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document.write( "you will use the 3 concepts shown above to solve this problem.\r<BR>\n" );
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document.write( "your equation is:<BR>\n" );
document.write( "log(3x-1)=log(x-3)+log(6)\r<BR>\n" );
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document.write( "you use the first concept to transform the right side of this equation to get:<BR>\n" );
document.write( "log(3x-1) = log((x-3)*6) which becomes:<BR>\n" );
document.write( "log(3x-1) = log(6x-18)\r<BR>\n" );
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document.write( "you then subtract the expression on the right side of the equation from both sides of the equation to get:<BR>\n" );
document.write( "log(3x-1) - log(6x-18) = 0\r<BR>\n" );
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document.write( "you then use the second concept to transform the left side of this equation to get:<BR>\n" );
document.write( "log((3x-1)/(6x-18)) = 0\r<BR>\n" );
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document.write( "you then apply the third concept to transform this equation to get:\r<BR>\n" );
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document.write( "log((3x-1)/(6x-18)) = 0 if and only if:<BR>\n" );
document.write( "10^0 = (3x-1)/(6x-18)\r<BR>\n" );
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document.write( "since 10^0 equals 1, then this equation becomes:<BR>\n" );
document.write( "(3x-1)/(6x-18) = 1\r<BR>\n" );
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document.write( "you then multiply both sides of this equation by (6x-18) to get:<BR>\n" );
document.write( "3x-1 = 6x-18\r<BR>\n" );
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document.write( "you then add 18 to both sides of this equation and subtract 3x from both sides of this equation to get:<BR>\n" );
document.write( "-1+18 = 6x-3x\r<BR>\n" );
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document.write( "you then combine like terms to get:\r<BR>\n" );
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document.write( "17 = 3x\r<BR>\n" );
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document.write( "you then divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "x = 17/3\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "you then substitute for x in your original equation and solve to confirm that this answer is good.\r<BR>\n" );
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document.write( "i did so using my calculator and confirmed that it's good.\r<BR>\n" );
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document.write( "my hand written calculations are shown below:<BR>\n" );
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document.write( " </SPAN>\n" );
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