document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=604786>Question 604786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for x. Round your answer to two decimal places, and do not include 'x' in answer?<BR>\n" );
document.write( "6*4^x=99 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381392 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=381392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given to solve for x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A4%5Ex=99 ALIGN=MIDDLE  ALT=\"6%2A4%5Ex=99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First, take the base 10 log of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2A4%5Ex%29+=+log%2899%29 ALIGN=MIDDLE  ALT=\"log%286%2A4%5Ex%29+=+log%2899%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using the product rule for logarithms, split the left side into two logarithms:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%29+%2B+log%284%5Ex%29+=+log%2899%29 ALIGN=MIDDLE  ALT=\"log%286%29+%2B+log%284%5Ex%29+=+log%2899%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract log(6) from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%284%5Ex%29+=+log%2899%29+-+log%286%29 ALIGN=MIDDLE  ALT=\"log+%284%5Ex%29+=+log%2899%29+-+log%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the rules for logarithms, an exponent can be brought outside as a multiplier. Therefore, on the left side, bring the x out as a multiplier of the logarithm. The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%284%29+=+log%2899%29+-+log%286%29 ALIGN=MIDDLE  ALT=\"x%2Alog%284%29+=+log%2899%29+-+log%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by log(4):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28log%2899%29+-+log%286%29%29%2Flog%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28log%2899%29+-+log%286%29%29%2Flog%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use a calculator to find that log(99) = 1.995635195, log(6) =  0.77815125, and log(4) = 0.602059991. Substitute these values into the equation for x to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281.995635195+-+0.77815125%29%2F0.602059991 ALIGN=MIDDLE  ALT=\"x+=+%281.995635195+-+0.77815125%29%2F0.602059991\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract the two terms on the numerator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.217483945%2F0.602059991 ALIGN=MIDDLE  ALT=\"x+=+1.217483945%2F0.602059991\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the division on the right side and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.022197062 ALIGN=MIDDLE  ALT=\"x+=+2.022197062\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem tells you to round this answer to two decimal places. When you do that, the answer shortens to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.02 ALIGN=MIDDLE  ALT=\"x+=+2.02\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer that you're looking for. Hope this helps you to understand the process and the rules that apply to logarithms better.<BR>\n" );
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