document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240665>Question 240665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express in logarithmic form of 64½=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176299 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The definition of logarithms states:\r<BR>\n" );
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document.write( "log(b,x) = y if and only if b^y = x\r<BR>\n" );
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document.write( "and:\r<BR>\n" );
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document.write( "b^y = x if and only if log(b,x) = y\r<BR>\n" );
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document.write( "Since 1/2 = .5, your formula becomes:\r<BR>\n" );
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document.write( "64^(.5) = 8\r<BR>\n" );
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document.write( "If we let:\r<BR>\n" );
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document.write( "64 = b<BR>\n" );
document.write( ".5 = y<BR>\n" );
document.write( "8 = x\r<BR>\n" );
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document.write( "Then, the definition of logarithms applied to your formula states:\r<BR>\n" );
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document.write( "64^(.5) = 8 if and only if log(64,8) = .5.\r<BR>\n" );
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document.write( "Algebra.com formula generator make it look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%5E%28%28.5%29%29+=+8 ALIGN=MIDDLE  ALT=\"64%5E%28%28.5%29%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2864%2C%288%29%29+=+.5 ALIGN=MIDDLE  ALT=\"log%2864%2C%288%29%29+=+.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you put 64^(.5) in your calculator, you will get 8.\r<BR>\n" );
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document.write( "If you put log(8)/log(64) in your calculator, you will get .5\r<BR>\n" );
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document.write( "log(8)/log(64) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2864%2C8%29 ALIGN=MIDDLE  ALT=\"log%2864%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means log of 8 to the base of 64.\r<BR>\n" );
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document.write( "The procedure uses the change of base of logarithm formula of:\r<BR>\n" );
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document.write( "This formula states that if you have a logarithm of a number to the base of b, and you want to convert it to a logarithm of the same number to the base of c, you take the logarithm of the number to the base of c and you divide it by the logarithm of the base of b to the base of c.\r<BR>\n" );
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document.write( "In your problem, we converted your exponential equation to the logarithmic form to get:\r<BR>\n" );
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document.write( "log of 8 to the base of 64 = .5\r<BR>\n" );
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document.write( "to prove that was true using the calculator, we had to convert the logarithm to the base of 64 to a logarithm to the base of 10 because the LOG function of the calculator works to the base of 10.\r<BR>\n" );
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document.write( "The formula we used was the change of base formula.\r<BR>\n" );
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document.write( "We took the logarithm of 8 to the base of 64 and converted it to the logarithm of 8 to the base as shown below:\r<BR>\n" );
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document.write( "log of 8 to the base of 64 = log of 8 to the base of 10 divided by the log of 64 to the base of 10.\r<BR>\n" );
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document.write( "this became:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2864%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C64%29 ALIGN=MIDDLE  ALT=\"log%2864%2C8%29+=+log%2810%2C8%29%2Flog%2810%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > making the result = .5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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