document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206117>Question 1206117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need help solving this equation. I am supposed to show all steps to solve for x. \r<BR>\n" );
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document.write( "log_(3)x+log_(3)(x+5)=9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843354 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28x%29%29%2Blog%283%2C%28x%2B5%29%29+=+9 ALIGN=MIDDLE  ALT=\"log%283%2C%28x%29%29%2Blog%283%2C%28x%2B5%29%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%28x%28x%2B5%29%29%29+=+9 ALIGN=MIDDLE  ALT=\"log%283%2C%28x%28x%2B5%29%29%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > use log rule that log(A)+log(B) = log(A*B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B5%29+=+3%5E9 ALIGN=MIDDLE  ALT=\"x%28x%2B5%29+=+3%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > convert from log form to exponent form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B5%29+=+19683 ALIGN=MIDDLE  ALT=\"x%28x%2B5%29+=+19683\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x+=+19683 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x+=+19683\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-19683+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-19683+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply the quadratic formula where a = 1, b = 5, c = -19683<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2B-sqrt%28%285%29%5E2-4%281%29%28-19683%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2B-sqrt%28%285%29%5E2-4%281%29%28-19683%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2B-sqrt%2825+%2B+78732%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2B-sqrt%2825+%2B+78732%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2B-sqrt%2878757%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2B-sqrt%2878757%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2Bsqrt%2878757%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2Bsqrt%2878757%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5-sqrt%2878757%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5-sqrt%2878757%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+137.818388 ALIGN=MIDDLE  ALT=\"x+=+137.818388\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-142.818388 ALIGN=MIDDLE  ALT=\"x+=+-142.818388\"   DISABLED_style= \"max-width:90%; height:auto;\" > both of which are approximate\r<BR>\n" );
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document.write( "Since the domain of log(x) is x > 0, it rules out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5-sqrt%2878757%29%29%2F%282%29+=+-142.818388 ALIGN=MIDDLE  ALT=\"x+=+%28-5-sqrt%2878757%29%29%2F%282%29+=+-142.818388\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a possible solution.\r<BR>\n" );
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document.write( "Therefore, we go with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2Bsqrt%2878757%29%29%2F%282%29+=+137.818388 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2Bsqrt%2878757%29%29%2F%282%29+=+137.818388\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the only possible solution.\r<BR>\n" );
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document.write( "I used WolframAlpha to confirm the answer is correct.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.wolframalpha.com/input?i=log_%283%29x%2Blog_%283%29%28x%2B5%29%3D9\">https://www.wolframalpha.com/input?i=log_%283%29x%2Blog_%283%29%28x%2B5%29%3D9</a>\r<BR>\n" );
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document.write( "Another way to confirm the answer is to let<BR>\n" );
document.write( "f(x) = log(x)/log(3) + log(x+5)/log(3)<BR>\n" );
document.write( "Note the use of the change of base formula.<BR>\n" );
document.write( "Then you should find that f(137.818388) = 9 approximately.<BR>\n" );
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