document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127474>Question 127474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the value of logbase2 (1/sqrt32? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93397 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=93397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set up the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%282%2C%281%2F%28sqrt%2832%29%29%29%29 ALIGN=MIDDLE  ALT=\"y+=+log%282%2C%281%2F%28sqrt%2832%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%2832%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to a number by using a calculator to divide the square root of 32 <BR>\n" );
document.write( "into 1. The answer to this division is 0.176776695. Substitute this into the equation <BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%282%2C0.176776695%29 ALIGN=MIDDLE  ALT=\"y+=+log%282%2C0.176776695%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get this into a little more conventional form by transposing (or switching) sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%282%2C0.176776695%29+=+y ALIGN=MIDDLE  ALT=\"+log%282%2C0.176776695%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now convert this logarithmic form to its equivalent form by raising the base of the logarithm<BR>\n" );
document.write( "(the base being 2) to the y power and setting this equal to 0.176776695. In other words<BR>\n" );
document.write( "you are converting the above logarithmic equation to the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey+=+0.176776695 ALIGN=MIDDLE  ALT=\"2%5Ey+=+0.176776695\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then take the logarithm of both sides ... only this time let's use base 10 as the logarithm<BR>\n" );
document.write( "because we can work in base 10 on a calculator. When you take the logarithm base 10 of both<BR>\n" );
document.write( "sides the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%5Ey%29+=+log%2810%2C0.176776695%29 ALIGN=MIDDLE  ALT=\"log%2810%2C2%5Ey%29+=+log%2810%2C0.176776695%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side of this equation, use the exponent rule of logarithms to bring out the <BR>\n" );
document.write( "exponent y as a multiplier of the logarithm. This results in the equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%2810%2C2%29+=+log%2810%2C0.176776695%29 ALIGN=MIDDLE  ALT=\"y%2Alog%2810%2C2%29+=+log%2810%2C0.176776695%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now use your calculator to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C0.176776695%29+=+-0.752574989 ALIGN=MIDDLE  ALT=\"log%2810%2C0.176776695%29+=+-0.752574989\"   DISABLED_style= \"max-width:90%; height:auto;\" > and also<BR>\n" );
document.write( "to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%29+=+0.301029995 ALIGN=MIDDLE  ALT=\"log%2810%2C2%29+=+0.301029995\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Substitute these numbers into the equation in place of their logarithm forms and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2A0.301029995+=+-0.752574989 ALIGN=MIDDLE  ALT=\"y%2A0.301029995+=+-0.752574989\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for y by dividing both sides of this equation by 0.301029995 and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-0.752574989%2F0.301029995+=+-2.5 ALIGN=MIDDLE  ALT=\"y+=+-0.752574989%2F0.301029995+=+-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And recall way back at the start of this exercise we said that y was equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%281%2Fsqrt%2832%29%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%281%2Fsqrt%2832%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So we can now say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%281%2Fsqrt%2832%29%29%29=+-2.5 ALIGN=MIDDLE  ALT=\"log%282%2C%281%2Fsqrt%2832%29%29%29=+-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the answer to this problem is -2.5<BR>\n" );
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document.write( "Hope this helps you to understand the problem and one way of doing it. The process that<BR>\n" );
document.write( "was used above to solve the problem essentially was the same process you use to develop the<BR>\n" );
document.write( "change of base formula that you might be familiar with. <BR>\n" );
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document.write( " </SPAN>\n" );
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