document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012071>Question 1012071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> So the question is as follows:\r<BR>\n" );
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document.write( "\"If log 2 + 0.301 and log 3 + 0.447, find each of the following using only these values and the properties of logarithms. Show your work.\r<BR>\n" );
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document.write( "a. log 6<BR>\n" );
document.write( "b. log (2/3)<BR>\n" );
document.write( "c. log 1.5<BR>\n" );
document.write( "d. log 18\"\r<BR>\n" );
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document.write( "my teacher stopped teaching the lessons because we have a limited time before exams, so she started assigning videos to watch. I watched the assigned ones, and many more but I just don't understand the question, I don't even really know what it's asking me to do. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627924 by </B><A HREF=/tutors/aboutme.mpl?userid=ValorousDawn><B>ValorousDawn(53)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ValorousDawn><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=ValorousDawn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there. I'm sorry to hear about your situation, let me try my best.<BR>\n" );
document.write( "Luckily, there's not a lot you have to know for these problems, but here's what you do have to know.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28ab%29=log%28a%29%2Blog%28b%29 ALIGN=MIDDLE  ALT=\"log%28ab%29=log%28a%29%2Blog%28b%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%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( "<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( "With this, we can tackle the problems.\r<BR>\n" );
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document.write( "Six is really just 2 times 3, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%29=log%282%2A3%29 ALIGN=MIDDLE  ALT=\"log%286%29=log%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We have from our first identity that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28ab%29=log%28a%29%2Blog%28b%29 ALIGN=MIDDLE  ALT=\"log%28ab%29=log%28a%29%2Blog%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A3%29=log%282%29%2Blog%283%29 ALIGN=MIDDLE  ALT=\"log%282%2A3%29=log%282%29%2Blog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We know these values, and we can then use substitution. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2Blog%283%29=0.301%2B0.447=0.748 ALIGN=MIDDLE  ALT=\"log%282%29%2Blog%283%29=0.301%2B0.447=0.748\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The second one is easier, as 2/3 is really straightforward. We use the identity <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;\" > here. We plug in a as 2 and b as 3 because they are the numerator and denominator respectively. We get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2F3%29=log%282%29-log%283%29 ALIGN=MIDDLE  ALT=\"log%282%2F3%29=log%282%29-log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then we can use substitution of values to solve. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29-log%283%29=0.301-0.447=-0.146 ALIGN=MIDDLE  ALT=\"log%282%29-log%283%29=0.301-0.447=-0.146\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Don't get tricked up on the third one because it's a decimal, remember that 1.5 is the same thing as 3/2 in fractional form. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%281.5%29=log%283%2F2%29 ALIGN=MIDDLE  ALT=\"log%281.5%29=log%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We use the same identity as above. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2F2%29=log%283%29-log%282%29 ALIGN=MIDDLE  ALT=\"log%283%2F2%29=log%283%29-log%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29-log%282%29=0.447-0.301=0.146 ALIGN=MIDDLE  ALT=\"log%283%29-log%282%29=0.447-0.301=0.146\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This one's a bit harder, but we just have to go back to the basics. Factorize, and you'll get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=2%2A3%5E2 ALIGN=MIDDLE  ALT=\"18=2%2A3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2818%29=log%282%2A3%5E2%29 ALIGN=MIDDLE  ALT=\"log%2818%29=log%282%2A3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can break it apart. We get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2A3%5E2%29=log%282%29%2Blog%283%5E2%29 ALIGN=MIDDLE  ALT=\"log%282%2A3%5E2%29=log%282%29%2Blog%283%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which due to <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;\" >, becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2Blog%283%5E2%29=log%282%29%2B2%2Alog%283%29 ALIGN=MIDDLE  ALT=\"log%282%29%2Blog%283%5E2%29=log%282%29%2B2%2Alog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute in your values, and you're done. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%29%2B2%2Alog%283%29=0.301%2B2%280.447%29=1.195 ALIGN=MIDDLE  ALT=\"log%282%29%2B2%2Alog%283%29=0.301%2B2%280.447%29=1.195\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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