document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=563670>Question 563670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this.  I can't understand the way my teacher is trying to explain.\r<BR>\n" );
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document.write( "Let \"b\" be a number such that log(b)3 = 1.5 and log(b)5=2.2<BR>\n" );
document.write( "evaluate the following:\r<BR>\n" );
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document.write( "1.  log (b)5/3<BR>\n" );
document.write( "2.  log (b)3b^2<BR>\n" );
document.write( "3.  log (b)45<BR>\n" );
document.write( "4.  log (b)(b/15)\r<BR>\n" );
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document.write( "Thank you so much for your help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364983 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is just making use of general rules of logs:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29+ ALIGN=MIDDLE  ALT=\"+log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%2Fb%29+=+log%28a%29++-+log%28b%29+ ALIGN=MIDDLE  ALT=\"+log%28a%2Fb%29+=+log%28a%29++-+log%28b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%5Eb%29+=+b%2Alog%28a%29+ ALIGN=MIDDLE  ALT=\"+log%28a%5Eb%29+=+b%2Alog%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28b%2Cb%29+=+1+ ALIGN=MIDDLE  ALT=\"+log%28b%2Cb%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All these rules can use any base for the logs<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C3+%29+=+1.5+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C3+%29+=+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C5+%29+=+2.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C5+%29+=+2.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C5%2F3+%29+=+log%28+b%2C5+%29+-+log%28+b%2C3+%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C5%2F3+%29+=+log%28+b%2C5+%29+-+log%28+b%2C3+%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%28+b%2C5%2F3+%29+=+2.2+-+1.5+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C5%2F3+%29+=+2.2+-+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C5%2F3+%29+=+.7+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C5%2F3+%29+=+.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C3b%5E2+%29+=+log%28b%2C3%29+%2B+2%2Alog%28b%2Cb%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C3b%5E2+%29+=+log%28b%2C3%29+%2B+2%2Alog%28b%2Cb%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%28+b%2C3b%5E2+%29+=+1.5+%2B+2%2A1+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C3b%5E2+%29+=+1.5+%2B+2%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C3b%5E2+%29+=+3.5+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C3b%5E2+%29+=+3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C45+%29+=+log%28b%2C9%29+%2B+log%28b%2C5%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C45+%29+=+log%28b%2C9%29+%2B+log%28b%2C5%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%28+b%2C45+%29+=+log%28b%2C3%5E2%29+%2B+2.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C45+%29+=+log%28b%2C3%5E2%29+%2B+2.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C45+%29+=+2%2Alog%28b%2C3%29+%2B+2.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C45+%29+=+2%2Alog%28b%2C3%29+%2B+2.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C45+%29+=+2%2A1.5+%2B+2.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C45+%29+=+2%2A1.5+%2B+2.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2C45+%29+=+5.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2C45+%29+=+5.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2Cb%2F15+%29+=+log%28+b%2Cb+%29+-+log%28+b%2C15+%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+log%28+b%2Cb+%29+-+log%28+b%2C15+%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%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3%2A5+%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3%2A5+%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%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3+%29+-+log%28+b%2C5+%29+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3+%29+-+log%28+b%2C5+%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%28+b%2Cb%2F15+%29+=+1+-+1.5+-+2.2+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+1+-+1.5+-+2.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2Cb%2F15+%29+=+1+-+3.7+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+1+-+3.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+b%2Cb%2F15+%29+=+-2.7+ ALIGN=MIDDLE  ALT=\"+log%28+b%2Cb%2F15+%29+=+-2.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );