document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956322>Question 956322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log&#8323; 6 + log&#8323; (3x + 1) = 21  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584246 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=584246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log3(6) + log3(3x+1) = 21\r<BR>\n" );
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document.write( "log3(6) + log(3x+1) is the same as log3(6 * (3x+1)) which is the same as:\r<BR>\n" );
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document.write( "log3(18x + 6)\r<BR>\n" );
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document.write( "your equation becomes log3(18x+6) = 21\r<BR>\n" );
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document.write( "this is true if and only if 3^21 = 18x + 6\r<BR>\n" );
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document.write( "subtract 6 from both sides of this equation to get:\r<BR>\n" );
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document.write( "3^21 - 6 = 18x\r<BR>\n" );
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document.write( "divide both sides of this equation by 18 to get:\r<BR>\n" );
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document.write( "(3^21 - 6) / 18 = x\r<BR>\n" );
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document.write( "solve for x to get x = 581130733.2\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "replace x with 581130733.2 in the original equation to get:\r<BR>\n" );
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document.write( "log3(6) + log3(3*581130733.2+1) = 21\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "log3(6) + log3(1743392201) = 21\r<BR>\n" );
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document.write( "convert log base 3 to log base 10 using the conversion formula of log3(a) = log10(a)/log10(3) which can also be shown as log(a)/log(3).\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "log(6)/log(3) + log(1743392201)/log(3) = 21\r<BR>\n" );
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document.write( "use your calculator log function to evaluate this equation to get:\r<BR>\n" );
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document.write( "21 = 21\r<BR>\n" );
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document.write( "this conforms your solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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