document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286328>Question 286328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express logarithm of log base c 5= a and log base c 4 =b \r<BR>\n" );
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document.write( "find log base c of 2\r<BR>\n" );
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document.write( "and log base c of 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207893 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=207893\">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=log%28c%2C+%285%29%29+=+a ALIGN=MIDDLE  ALT=\"log%28c%2C+%285%29%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%284%29%29+=+b ALIGN=MIDDLE  ALT=\"log%28c%2C+%284%29%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will need to use the properties on the base c logarithms we have. There are properties for products, quotients and powers of arguments. Since 4 is a power of 2 we can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%284%29%29+=+b ALIGN=MIDDLE  ALT=\"log%28c%2C+%284%29%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the property about powers in the argument of a logarithm to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%284%29%29+=+b ALIGN=MIDDLE  ALT=\"log%28c%2C+%284%29%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%5E2%29%29+=+b ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%5E2%29%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the property, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C+%28p%5Eq%29%29+=+q%2Alog%28x%2C+%28q%29%29 ALIGN=MIDDLE  ALT=\"log%28x%2C+%28p%5Eq%29%29+=+q%2Alog%28x%2C+%28q%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to move the exponent out of the argument:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%28c%2C+%282%29%29+=+b ALIGN=MIDDLE  ALT=\"2log%28c%2C+%282%29%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we jsut divide by two:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%29%29+=+b%2F2 ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%29%29+=+b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We now have three base c logarithms. For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%2810%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we look for a product, quotient or power of 2, 4 and/or 5 which makes 10. Obviously 2*5=10 so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%2810%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%2A5%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%2A5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can use the property for products in an argument, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C+%28p%2Aq%29%29+=+log%28x%2C+%28p%29%29+%2B+log%28x%2C+%28q%29%29 ALIGN=MIDDLE  ALT=\"log%28x%2C+%28p%2Aq%29%29+=+log%28x%2C+%28p%29%29+%2B+log%28x%2C+%28q%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to separate the 2 and the 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28c%2C+%282%29%29+%2B+log%28c%2C+%285%29%29 ALIGN=MIDDLE  ALT=\"log%28c%2C+%282%29%29+%2B+log%28c%2C+%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can replace these logarithms with what we know them to be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2+%2B+a ALIGN=MIDDLE  ALT=\"b%2F2+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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