document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32682>Question 32682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each of the following equations either prove that it is correct (by using the rules of logarithms and exponents) or else show that it is not correct (by finding numerical values for the variables that make the values of the two sides of the equation different).\r<BR>\n" );
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document.write( "log (x/y) = log x/ log y<BR>\n" );
document.write( "log x - log y = log (x/y)<BR>\n" );
document.write( "log (2x) = 2 log x<BR>\n" );
document.write( "2 log x = log (x^2)<BR>\n" );
document.write( "log x+1 / x+3 = log (x+1) - log (x+3)<BR>\n" );
document.write( "log (x square root x^2 + 1) = log x + 1/2 (x^2 +1)<BR>\n" );
document.write( "log (x^2 +1) = 2 log x + log 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20094 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For each of the following equations either prove that it is correct (by using the rules of logarithms and exponents) or else show that it is not correct (by finding numerical values for the variables that make the values of the two sides of the equation different).<BR>\n" );
document.write( "log (x/y) = log x/ log y<BR>\n" );
document.write( "LHS....LOG(10/1)=LOG(10)=1...BUT RHS... LOG(10)/LOG(10)=1/0.....NOT CORRECT<BR>\n" );
document.write( "log x - log y = log (x/y)<BR>\n" );
document.write( "OK..AS PER FORMULA..<BR>\n" );
document.write( "log (2x) = 2 log x<BR>\n" );
document.write( "LHS.....LOG(2*1)=LOG(2).....RHS....2*LOG(1)=2*0=0....NOT CORRECT<BR>\n" );
document.write( "2 log x = log (x^2)<BR>\n" );
document.write( "CORRECT AS PER FORMULA  LOG(X)^N=N*LOG(X)<BR>\n" );
document.write( "log {(x+1) / (x+3)} = log (x+1) - log (x+3)...I SUPPOSE THIS IS THE PROBLEM.<BR>\n" );
document.write( "CORRECT AS PER FORMULA...LOG(A/B)=LOG(A)-LOG(B)<BR>\n" );
document.write( "log {(x *square root (x^2 + 1)} = log x + 1/2 (x^2 +1)<BR>\n" );
document.write( "WRONG...LHS....LOG{1*SQRT(1^2+1)}=LOG{SQRT(2)}<BR>\n" );
document.write( "RHS......LOG(1)+(1/2)*(1+1)=0+1=1...WHICH IS NOT CORRECT.\r<BR>\n" );
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document.write( "log (x^2 +1) = 2 log x + log 1<BR>\n" );
document.write( "WRONG...LHS.....LOG(1^2+1)=LOG(2)<BR>\n" );
document.write( "RHS.....2*LOG(1)+LOG(1)=0+0=0.......WHICH IS NOT CORRECT... </SPAN>\n" );
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