document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205369>Question 1205369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if log10^2=0.3010 and log10 ^7=0.8451.Evaluate \"1\" log10 ^0.2 \"2\" log10^35^2 without using tables or calculator .Evaluate<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842115 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=842115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "Each log shown below is base 10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%282%29%29+=+0.3010 ALIGN=MIDDLE  ALT=\"log%28%282%29%29+=+0.3010\"   DISABLED_style= \"max-width:90%; height:auto;\" > (given)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287%29%29+=+0.8451 ALIGN=MIDDLE  ALT=\"log%28%287%29%29+=+0.8451\"   DISABLED_style= \"max-width:90%; height:auto;\" > (given)\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%280.2%29%29+=+log%28%282%2F10%29%29 ALIGN=MIDDLE  ALT=\"log%28%280.2%29%29+=+log%28%282%2F10%29%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%28%280.2%29%29+=+log%28%282%29%29+-+log%28%2810%29%29 ALIGN=MIDDLE  ALT=\"log%28%280.2%29%29+=+log%28%282%29%29+-+log%28%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use log rule log(A/B) = log(A)-log(B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%280.2%29%29+=+0.3010+-+1 ALIGN=MIDDLE  ALT=\"log%28%280.2%29%29+=+0.3010+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule that log(10) = 1 where the log is base 10.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%280.2%29%29+=+-0.699 ALIGN=MIDDLE  ALT=\"log%28%280.2%29%29+=+-0.699\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is approximate.\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "Each log shown below is base 10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2Alog%28%2835%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2Alog%28%2835%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use log rule log(A^B) = B*log(A) to pull down the exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2Alog%28%285%2A7%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2Alog%28%285%2A7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 35 as 5*7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2A%28log%28%285%29%29%2Blog%28%287%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%28log%28%285%29%29%2Blog%28%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use log rule log(AB) = log(A)+log(B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2A%28log%28%2810%2F2%29%29%2Blog%28%287%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%28log%28%2810%2F2%29%29%2Blog%28%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the 5 as 10/2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2A%28log%28%2810%29%29+-+log%28%282%29%29%2Blog%28%287%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%28log%28%2810%29%29+-+log%28%282%29%29%2Blog%28%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use log rule log(A/B) = log(A)-log(B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2A%281+-+0.3010%2B0.8451%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%281+-+0.3010%2B0.8451%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given info; also log(10) = 1 when log is base 10.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+3.0882 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+3.0882\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately\r<BR>\n" );
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document.write( "Another approach for problem 2\r<BR>\n" );
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document.write( "Each log shown below is base 10.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+2%2Alog%28%2835%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2Alog%28%2835%29%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%28%2835%5E2%29%29+=+2%2Alog%28%28%2810%2F2%29%2A7%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2Alog%28%28%2810%2F2%29%2A7%29%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%28%2835%5E2%29%29+=+2%2Alog%28%287%2F%282%2F10%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2Alog%28%287%2F%282%2F10%29%29%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%28%2835%5E2%29%29+=+2%2A%28log%28%287%29%29+-+log%28%280.2%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%28log%28%287%29%29+-+log%28%280.2%29%29%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%28%2835%5E2%29%29+=+2%2A%280.8451+-+%28-0.699%29%29 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+2%2A%280.8451+-+%28-0.699%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in log(7) = 0.8451, and use the result of problem 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2835%5E2%29%29+=+3.0882 ALIGN=MIDDLE  ALT=\"log%28%2835%5E2%29%29+=+3.0882\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<BR>\n" );
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