document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140699>Question 140699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i solve log64^8=x\r<BR>\n" );
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document.write( "The answer is 1/2 but how do you come about that answer?\r<BR>\n" );
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document.write( "Also log5^1/5=x & log7^square root of 7=x\r<BR>\n" );
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document.write( "These have me so confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102402 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=102402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the problem looks like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2864%2C%288%29%29=x ALIGN=MIDDLE  ALT=\"log%2864%2C%288%29%29=x\"   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%2864%2C%288%29%29=x ALIGN=MIDDLE  ALT=\"log%2864%2C%288%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%288%29%29%2Flog%2810%2C%2864%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%288%29%29%2Flog%2810%2C%2864%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side by using the change of base formula. Remember the change of base formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%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%2810%2C%288%29%29%2Flog%2810%2C%288%5E2%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%288%29%29%2Flog%2810%2C%288%5E2%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 64 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2 ALIGN=MIDDLE  ALT=\"8%5E2\"   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%2810%2C%288%29%29%2F%282%2Alog%2810%2C%288%29%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%288%29%29%2F%282%2Alog%2810%2C%288%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the denominator using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%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=cross%28log%2810%2C%288%29%29%29%2F%282cross%28log%2810%2C%288%29%29%29%29=x ALIGN=MIDDLE  ALT=\"cross%28log%2810%2C%288%29%29%29%2F%282cross%28log%2810%2C%288%29%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide and cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=x ALIGN=MIDDLE  ALT=\"1%2F2=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   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%285%2C%281%2F5%29%29=x ALIGN=MIDDLE  ALT=\"log%285%2C%281%2F5%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281%2F5%29%29%2Flog%2810%2C%285%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29%2Flog%2810%2C%285%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side by using the change of base formula. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%281%2F5%29%29%2Flog%2810%2C%28%281%2F5%29%5E%28-1%29%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29%2Flog%2810%2C%28%281%2F5%29%5E%28-1%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 5 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=%281%2F5%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"5=%281%2F5%29%5E%28-1%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%2810%2C%281%2F5%29%29%2F%28-1%2Alog%2810%2C%281%2F5%29%29%29=x ALIGN=MIDDLE  ALT=\"log%2810%2C%281%2F5%29%29%2F%28-1%2Alog%2810%2C%281%2F5%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the denominator using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%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=cross%28log%2810%2C%281%2F5%29%29%29%2F%28-1%2Across%28log%2810%2C%281%2F5%29%29%29%29=x ALIGN=MIDDLE  ALT=\"cross%28log%2810%2C%281%2F5%29%29%29%2F%28-1%2Across%28log%2810%2C%281%2F5%29%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-1%29=x ALIGN=MIDDLE  ALT=\"1%2F%28-1%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   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%287%2C%28sqrt%287%29%29%29=x ALIGN=MIDDLE  ALT=\"log%287%2C%28sqrt%287%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C%287%5E%281%2F2%29%29%29=x ALIGN=MIDDLE  ALT=\"log%287%2C%287%5E%281%2F2%29%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"7%5E%281%2F2%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=%281%2F2%29%2Alog%287%2C%287%29%29=x ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Alog%287%2C%287%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expression using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%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=%281%2F2%29%2A1=x ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A1=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log base 7 of 7 to get 1. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C%287%29%29=1 ALIGN=MIDDLE  ALT=\"log%287%2C%287%29%29=1\"   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=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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