document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375676>Question 375676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given log(base\"a\")2=x, determine log(base\"16)(a^log(base\"a\")x)=100. Solve for a.\r<BR>\n" );
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document.write( "I have simplified the question to (4x)(a^log(base\"a\")x)=100. I am not sure what I can now do to solve for \"a\". </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267246 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=267246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%282%29%29+=x ALIGN=MIDDLE  ALT=\"log%28a%2C+%282%29%29+=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2816%2C%28a%5Elog%28a%2C+%28x%29%29%29%29=100 ALIGN=MIDDLE  ALT=\"log%2816%2C%28a%5Elog%28a%2C+%28x%29%29%29%29=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Let's start by looking at: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Elog%28a%2C+%28x%29%29 ALIGN=MIDDLE  ALT=\"a%5Elog%28a%2C+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Once you understand logarithms well you will see instantly how this simplifies. The exponent, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is a logarithm. Logarithms are exponents. This logarithm represents \"the exponent for \"a\" that results in \"x\". And where do we find this exponent? Answer: As the exponent for \"a\"! So by definition, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Elog%28a%2C+%28x%29%29 ALIGN=MIDDLE  ALT=\"a%5Elog%28a%2C+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is x! The second equation is now:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2816%2C%28x%29%29=100 ALIGN=MIDDLE  ALT=\"log%2816%2C%28x%29%29=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Into this equation we can substitute for x using the first equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2816%2C%28log%28a%2C+%282%29%29%29%29=100 ALIGN=MIDDLE  ALT=\"log%2816%2C%28log%28a%2C+%282%29%29%29%29=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We now have an equation with just a in it. We can now solve for a, First we rewrite the equation in exponential form. In general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28z%2C+%28p%29%29+=+q ALIGN=MIDDLE  ALT=\"log%28z%2C+%28p%29%29+=+q\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+z%5Eq ALIGN=MIDDLE  ALT=\"p+=+z%5Eq\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using this on the equation above we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%282%29%29=+16%5E100 ALIGN=MIDDLE  ALT=\"log%28a%2C+%282%29%29=+16%5E100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rewriting this equation in exponential form we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+a%5E%2816%5E100%29 ALIGN=MIDDLE  ALT=\"2+=+a%5E%2816%5E100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And last we find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E100 ALIGN=MIDDLE  ALT=\"16%5E100\"   DISABLED_style= \"max-width:90%; height:auto;\" >th root of each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28%2816%5E100%29%2C+2%29+=+a ALIGN=MIDDLE  ALT=\"root%28%2816%5E100%29%2C+2%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Since \"a\" was the base of a logarithm it had to be positive. So we do not need to be concerned with the negative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E100 ALIGN=MIDDLE  ALT=\"16%5E100\"   DISABLED_style= \"max-width:90%; height:auto;\" >th root of 2.)<br><BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E100 ALIGN=MIDDLE  ALT=\"16%5E100\"   DISABLED_style= \"max-width:90%; height:auto;\" >th root of 2 is a very strange answer. Perhaps you made a mistake in posting this problem. I have checked my work and I do not see any mistakes.\r<BR>\n" );
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