document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843561>Question 843561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each equation. Show all your work. Round your answers to four decimal places.<BR>\n" );
document.write( "a. 	63x = 104<BR>\n" );
document.write( "b.	log3(x + 2) + log3(4x – 1) = 5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508234 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=508234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 63x = 104<BR>\n" );
document.write( "divide both sides of this equation by 63 to get:<BR>\n" );
document.write( "x = 104/63\r<BR>\n" );
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document.write( "log3(x+2) + log3(4x-1) = 5<BR>\n" );
document.write( "use the log property of log(a) + log(b) = log(a*b) to get:<BR>\n" );
document.write( "log3((x+2)*(4x-1)) = 5<BR>\n" );
document.write( "simplify the expression within the log to get:<BR>\n" );
document.write( "log3(4x^2 + 7x - 2) = 5<BR>\n" );
document.write( "the basic property of logs states that logb(x) = y if and only if b^y = x<BR>\n" );
document.write( "apply this property to the equation to get:<BR>\n" );
document.write( "3^5 = 4x^2 + 7x - 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "243 = 4x^2 + 7x - 2<BR>\n" );
document.write( "subtract 243 from both sides of this equation to get:<BR>\n" );
document.write( "0 = 4x^2 + 7x - 245<BR>\n" );
document.write( "commute this equation to get:<BR>\n" );
document.write( "4x^2 + 7x - 245 = 0<BR>\n" );
document.write( "factor this equation by using the quadratic formula to get:<BR>\n" );
document.write( "x = (-7 +/- sqrt(3969)) / 8.<BR>\n" );
document.write( "this simplifies to:<BR>\n" );
document.write( "x = (-7 +/- 63) / 8<BR>\n" );
document.write( "your solutions are:<BR>\n" );
document.write( "x = 7<BR>\n" );
document.write( "x = -8.75\r<BR>\n" );
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document.write( "since you can't take the log of a negative number, the solution of x = -8.75 is not good.<BR>\n" );
document.write( "the only solution left is x = 7.\r<BR>\n" );
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document.write( "you would need to confirm this solution is good by replacing x with 7 in the original equation to see if the equation is true.\r<BR>\n" );
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document.write( "the original equation is:<BR>\n" );
document.write( "log3(x+2) + log(3(4x-1) = 5<BR>\n" );
document.write( "replace x with 7 and simplify to get:<BR>\n" );
document.write( "log3(9) + log3(27) = 5\r<BR>\n" );
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document.write( "log3(9) = y if and only if 3^y = 9<BR>\n" );
document.write( "this makes y = 2, so log3(9) = 2\r<BR>\n" );
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document.write( "similarly, log3(27) = y if and only if 3^6 = 27<BR>\n" );
document.write( "this makes y = 3, so log3(27) = 3\r<BR>\n" );
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document.write( "your equation of:<BR>\n" );
document.write( "log3(9) + log3(27) = 5 becomes:<BR>\n" );
document.write( "2 + 3 = 5 which is true.\r<BR>\n" );
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document.write( "this confirms the solution is good.<BR>\n" );
document.write( "x = 7 is your solution.\r<BR>\n" );
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