document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209209>Question 1209209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x = 2ᵅ and y = 4ⁿ, show clearly that log₂(x²y) = 3α + 2n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847841 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=847841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Log Rules<BR>\n" );
document.write( "log(M*N) = log(M)+log(N)<BR>\n" );
document.write( "log(M^N) = N*log(M)<BR>\n" );
document.write( "Let's refer to these as equations (1) and (2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%5Ea ALIGN=MIDDLE  ALT=\"x+=+2%5Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" > converts to the log form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%29%29+=+a ALIGN=MIDDLE  ALT=\"log%282%2C%28x%29%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll refer to this as equation (3)\r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4%5En ALIGN=MIDDLE  ALT=\"y+=+4%5En\"   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=y+=+%282%5E2%29%5En ALIGN=MIDDLE  ALT=\"y+=+%282%5E2%29%5En\"   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=y+=+2%5E%282n%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%282n%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=log%282%2C%28y%29%29+=+2n ALIGN=MIDDLE  ALT=\"log%282%2C%28y%29%29+=+2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Let's call this equation (4)\r<BR>\n" );
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document.write( "Then we would write the following<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2y%29%29+=+log%282%2C%28x%5E2%29%29%2Blog%282%2C%28y%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2y%29%29+=+log%282%2C%28x%5E2%29%29%2Blog%282%2C%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use equation (1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2y%29%29+=+2%2Alog%282%2C%28x%29%29%2Blog%282%2C%28y%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2y%29%29+=+2%2Alog%282%2C%28x%29%29%2Blog%282%2C%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use equation (2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2y%29%29+=+2a%2Blog%282%2C%28y%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2y%29%29+=+2a%2Blog%282%2C%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use equation (3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2y%29%29+=+2a%2B2n ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2y%29%29+=+2a%2B2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use equation (4)\r<BR>\n" );
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document.write( "I don't know where your teacher is getting the 3 in 3a.<BR>\n" );
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