document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475131>Question 475131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x: (9a^2b)^x(3ab)^4=9^5a^10b^7\r<BR>\n" );
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document.write( "I am not sure how to solve for x or even how to isolate it when it is an exponent. Especially when there are so many other variables(a, b) and a huge number (9 raised to the 5th power=59,049). There is just too much going on with this one for me to solve on my own.\r<BR>\n" );
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document.write( "Thank you in advance!\r<BR>\n" );
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document.write( "Jessica Ortiz </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325780 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Break everything in the LHS into pieces:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(9a^2b\right)^x\,\cdot\,\left(3ab\right)^4\ =\ 9^x\,\cdot\,a^{2x}\,\cdot\,b^x\,\cdot\,3^4\,\cdot\,a^4\,\cdot\,b^4\">\r<BR>\n" );
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document.write( "First thing to note is that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3^4\ =\ 3^2\,\cdot\,3^2\ =\ 9\,\cdot\,9\ =\ 9^2\">\r<BR>\n" );
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document.write( "Next, substitute and rearrange:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9^x\,\cdot\,9^2\,\cdot\,a^{2x}\,\cdot\,a^4\,\cdot\,b^x\,\cdot\,b^4\"> \r<BR>\n" );
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document.write( "Use the sum of exponents rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9^{x\,+\,2}\,\cdot\,a^{2x\,+\,4}\,\cdot\,b^{x\,+\,4}\">\r<BR>\n" );
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document.write( "Now this uglier-than-a-mud-fence expression is equivalent to the original Left Hand Side, which we were told was equal to the original right hand side, hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9^{x\,+\,2}\,\cdot\,a^{2x\,+\,4}\,\cdot\,b^{x\,+\,4}\ =\ 9^5\,\cdot\,a^{10}\,\cdot\,b^7\">\r<BR>\n" );
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document.write( "Now all we need to do is find a value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\ =\ 5\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\ +\ 4\ =\ 10\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 4\ =\ 7\">\r<BR>\n" );
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document.write( "Can you take it from here?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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