document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274524>Question 274524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x in the equation logxbase3 = 3*x-25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200324 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=200324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Clog%283%2Cx%29%2C3x-25%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Clog%283%2Cx%29%2C3x-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I don't think I've ever seen one like this before, but there is a solution as you can see from the graph.\r<BR>\n" );
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document.write( "What I did was make y = 3x-25.\r<BR>\n" );
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document.write( "since 3x-25 = log(3,x), then I also made another equation of y = log(3,x).\r<BR>\n" );
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document.write( "The intersection of those 2 equations is the solution.\r<BR>\n" );
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document.write( "That solution is somewhere around x = 9.\r<BR>\n" );
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document.write( "The original equation is:\r<BR>\n" );
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document.write( "log(3,x) = 3x-25\r<BR>\n" );
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document.write( "if x equal 9, then this equation becomes:\r<BR>\n" );
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document.write( "log(3,9) = 3*9 - 25 which becomes:\r<BR>\n" );
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document.write( "log(3,9) = 27-25 = 2\r<BR>\n" );
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document.write( "this is true if and only if 3^2 = 9 which it does, so the solution of x = 9 is good.\r<BR>\n" );
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document.write( "I still haven't been able to figure out how to derive it from the formula.\r<BR>\n" );
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document.write( "If x had to be an integer, then it would be a relatively simple matter of looking at different values of x until you found a solution.\r<BR>\n" );
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document.write( "The formula of log(3,x) = 3x-25 would be a clue that x had to be greater than 8 because the log of a number can't be negative.   3*8 = 24-25 = -1 would have been invalid, so you would have had to start at x = 9.  If so, you would have had it on the first go.\r<BR>\n" );
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document.write( "If x did not have to be an integer than that method for a solution would have been a lengthy process of interpolation until you narrowed into the actual solution.\r<BR>\n" );
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document.write( "Sorry I couldn't do any better.   Everything I tried turned into an identity which is not enough to solve the problem.\r<BR>\n" );
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document.write( "If you do find a solution algebraically, let me know.\r<BR>\n" );
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document.write( "In the meantime, I hope this helped a little.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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