document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=690131>Question 690131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I was wondering how you would solve the following;<BR>\n" );
document.write( "Log2(x)+log2(x-3)=2<BR>\n" );
document.write( "As well as that, I was wonder how to simplify the following;<BR>\n" );
document.write( "Log5(8)-log5(40)-log5(50)+log5(10)<BR>\n" );
document.write( "Thanks, Tom. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426183 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=426183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It takes me back about 64 years when I last used logs, but I'll try to remember.<BR>\n" );
document.write( "First use the formula, if<BR>\n" );
document.write( "(1) Logn(N) = x then<BR>\n" );
document.write( "(2) N = n^x<BR>\n" );
document.write( "I hope this is right, is it?<BR>\n" );
document.write( "Also, I know that<BR>\n" );
document.write( "(3) Logn(a) + Logn(b) = Logn(a*b).<BR>\n" );
document.write( "Using (3) on your problem yields<BR>\n" );
document.write( "(4) Log2(x*(x-3)) = 2<BR>\n" );
document.write( "Now use (2) on (4) we get<BR>\n" );
document.write( "(5) x*(x-3) = 2^2 or<BR>\n" );
document.write( "(6) x^2 - 3x -4 = 0, which factors to<BR>\n" );
document.write( "(7) (x-4)(x+1) = 0, which gives the set of roots<BR>\n" );
document.write( "(8) x = {4,-1}<BR>\n" );
document.write( "Let's check these values using the given equation.<BR>\n" );
document.write( "Is (Log2(4) + Log2(4-3) = 2)?<BR>\n" );
document.write( "Is (2 + 0 = 2)? Yes<BR>\n" );
document.write( "Is (Log2(-1*(-1-3)) = 2)?<BR>\n" );
document.write( "Is (Log2(4) = 2)?<BR>\n" );
document.write( "Is (4 = 2^2)?<BR>\n" );
document.write( "Is (4 = 4)? Yes<BR>\n" );
document.write( "Answer: The solution pair is x = {4,-1}<BR>\n" );
document.write( "We can use (3) to simplify your second problem to<BR>\n" );
document.write( "(9) Log5(8/40/50*10) or<BR>\n" );
document.write( "(10) Log5(1/5/50*10) or<BR>\n" );
document.write( "(11) Log5(1/250*10) or<BR>\n" );
document.write( "(12) Log5(1/25)<BR>\n" );
document.write( "Let y = (12) and<BR>\n" );
document.write( "Using (1) and (2) on (12) we get<BR>\n" );
document.write( "(13) 1/25 = 5^y or<BR>\n" );
document.write( "(14) y = -2<BR>\n" );
document.write( "Answer: Log5(8) - Log5(40) - Log5(50) + Log5(10) = -2. </SPAN>\n" );
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