document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131605>Question 1131605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If(y-1)log4 = ylog16, without using Mathematical table or calculator. Find the value of y.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748276 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=748276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "(y - 1) * log(4) = y * log(16).\r<BR>\n" );
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document.write( "y * log(16) is the same as y * log(4^2) which is the same as 2 * y * log(4).\r<BR>\n" );
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document.write( "your original equation becomes:\r<BR>\n" );
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document.write( "(y - 1) * log(4) = 2 * y * log(4)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(4) and you get:\r<BR>\n" );
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document.write( "y - 1 = 2 * y\r<BR>\n" );
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document.write( "subtract y from both sides of this equation and you get:\r<BR>\n" );
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document.write( "-1 = 2 * y - y\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "-1 = y\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "confirm by replacing y in the original equation to get:\r<BR>\n" );
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document.write( "(y - 1) * log(4) = y * log(16) becomes (-1 - 1) * log(4) = -1 * log(16)\r<BR>\n" );
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document.write( "simplify to get -2 * log(4) = -1 * log(16).\r<BR>\n" );
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document.write( "use your calculator to get -1.204119983 = -1.204119983.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "you did not use a calculator to solve this.<BR>\n" );
document.write( "you only used a calculator to confirm the solution is correct.\r<BR>\n" );
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document.write( "the key to solving this is to realize that log(16) = log(4^2) and to realize that log (4^2) = 2 * log(4).\r<BR>\n" );
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document.write( "the fact that log(4^2) = 2 * log(4) is one of the properties of logs.\r<BR>\n" );
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document.write( "here's a reference on the properties of logs.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html\" target = \"_blank\">http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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