document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4694>Question 4694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a couple of questions that I need help with:\r<BR>\n" );
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document.write( "1.  Solve for x:  <BR>\n" );
document.write( "    ln7 + ln(x-3) = ln(x + 15)\r<BR>\n" );
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document.write( "2.  Solve for x:<BR>\n" );
document.write( "    28 = 19 + 12^(x-7)<BR>\n" );
document.write( "    **The (x-7) is an exponent for the number 12\r<BR>\n" );
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document.write( "3.  Solve for x:  <BR>\n" );
document.write( "    e^(3x-4) = 1/e^(x-12)<BR>\n" );
document.write( "    **The (3x-4) and (x-12) are both exponents\r<BR>\n" );
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document.write( "4.  Use the properties of logarithms to write 3lnx^2 + ln(2x-4)-ln(3x-6) as a single logarithm.\r<BR>\n" );
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document.write( "To whoever is kind enough to help with answering these problems:  Thank you and I would appreciate it if you could show your work so I can better understand how to do these types of problems myself.  Thanks again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2201 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  ln7 + ln(x-3) = ln(x + 15)\r<BR>\n" );
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document.write( "First get the variables on one side (the right side) by subtracting ln(x-3) from each side.<BR>\n" );
document.write( "ln 7 = ln(x+15) - ln(x-3)\r<BR>\n" );
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document.write( "Use the property of logs to express the right side as a log of a single quantity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln+M+-+ln+N+=+ln+%28M%2FN%29+ ALIGN=MIDDLE  ALT=\"+ln+M+-+ln+N+=+ln+%28M%2FN%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+7+=+ln+%28%28x%2B15%29%2F%28x-3%29%29+ ALIGN=MIDDLE  ALT=\"ln+7+=+ln+%28%28x%2B15%29%2F%28x-3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because ln A = ln B, you can say that A=B.  In the same way,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%28x%2B15%29%2F%28x-3%29+ ALIGN=MIDDLE  ALT=\"7+=+%28x%2B15%29%2F%28x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides of the equation by (x-3):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x-3%29+=+%28x%2B+15%29+ ALIGN=MIDDLE  ALT=\"7%28x-3%29+=+%28x%2B+15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+-+21+=+x+%2B+15+ ALIGN=MIDDLE  ALT=\"7x+-+21+=+x+%2B+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+36 ALIGN=MIDDLE  ALT=\"6x+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check to make sure x= 6 doesn't give you the log of a negative.  It does not.\r<BR>\n" );
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document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28+=+19+%2B+12%5E%28x-7%29 ALIGN=MIDDLE  ALT=\"28+=+19+%2B+12%5E%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 19 from each side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+12%5E%28x-7%29 ALIGN=MIDDLE  ALT=\"9+=+12%5E%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the ln of each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%289%29+=+ln+%2812%5E%28x-7%29%29+ ALIGN=MIDDLE  ALT=\"ln+%289%29+=+ln+%2812%5E%28x-7%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By law of logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%289%29+=+%28x-7%29+%2A+ln+%2812%29 ALIGN=MIDDLE  ALT=\"ln+%289%29+=+%28x-7%29+%2A+ln+%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By distributive property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%289%29+=+x+ln%2812%29+-+7+ln%2812%29+ ALIGN=MIDDLE  ALT=\"ln+%289%29+=+x+ln%2812%29+-+7+ln%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 7 ln (12) to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%289%29+%2B+7+ln+%2812%29+=+x+ln+%2812%29+ ALIGN=MIDDLE  ALT=\"ln+%289%29+%2B+7+ln+%2812%29+=+x+ln+%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by ln (12)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28ln+%289%29+%2B+7+ln+%2812%29%29%2F+%28ln+%2812+%29%29+=+x+ ALIGN=MIDDLE  ALT=\"+%28ln+%289%29+%2B+7+ln+%2812%29%29%2F+%28ln+%2812+%29%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm very sorry, that's all I have time for.  Maybe someone else will do the others, or perhaps you can repost them.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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