document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074900>Question 1074900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve log8(5)-log8(2x)=log8(9) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689565 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=689565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with log8(5) - log8(2x) = log8(9)\r<BR>\n" );
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document.write( "subtract log8(5) from both sides to get -log8(2x) = log8(9) - log8(5)\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get log8(2x) = log8(5) - log8(9)\r<BR>\n" );
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document.write( "since log(x) - log(y) = log(x/y), you get log8(2x) = log8(5/9)\r<BR>\n" );
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document.write( "this is true if and only if 2x = 5/9.\r<BR>\n" );
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document.write( "solve for x to get x = 5/18.\r<BR>\n" );
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document.write( "confirm by replacing x with 5/18 in the original equation.\r<BR>\n" );
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document.write( "you get log8(5) - log8(2*5/18) = log8(9)\r<BR>\n" );
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document.write( "simplify to get log8(5) - log8(5/9) = log8(9)\r<BR>\n" );
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document.write( "since log(x) - log(y) = log(x/y), this becomes log8(5/(5/9)) = log8(9)\r<BR>\n" );
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document.write( "simplify to get log8(5*9/5) = log8(9)\r<BR>\n" );
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document.write( "simplify further to get log8(9) = log8(9).\r<BR>\n" );
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document.write( "you can also confirm by using the log base conversion formula of:\r<BR>\n" );
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document.write( "log8(x) = log(x)/log(8)\r<BR>\n" );
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document.write( "log(x) means log10(x) which is the LOG function of your calculator.\r<BR>\n" );
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document.write( "your original equation is:\r<BR>\n" );
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document.write( "log8(5) - log8(2x) = log8(9)\r<BR>\n" );
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document.write( "use the base conversion formula to get log(5)/log(8) - log(2x)/log(8) = log(9)/log(8)\r<BR>\n" );
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document.write( "multiply both sides of the equation by log(8) to get log(5) - log(2x) = log(9).\r<BR>\n" );
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document.write( "now you're in base 10 and you can use your calculator to confirm the solution.\r<BR>\n" );
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document.write( "your solution was x = 5/18 which made 2x = 5/9.\r<BR>\n" );
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document.write( "replace 2x with 5/9 and your equation in base 10 becomes log(5) - log(5/9) = log(9)\r<BR>\n" );
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document.write( "use your calculator to confirm.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "log(5) - log(5/9) = .9542425094<BR>\n" );
document.write( "log(9) = the same.\r<BR>\n" );
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document.write( "it didn't matter whether you were in base 10 or base 8.<BR>\n" );
document.write( "this equation was valid regardless of the base of the log.<BR>\n" );
document.write( "the reason is because log(x) = log(y) if and only if x = y.<BR>\n" );
document.write( "this fact was shown above in the statements:<BR>\n" );
document.write( "log8(2x) = log8(5/9)<BR>\n" );
document.write( "this is true if and only if 2x = 5/9.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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