document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30417>Question 30417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this problem.  Thank you.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C+k%29 ALIGN=MIDDLE  ALT=\"log%28x%2C+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C+x%29 ALIGN=MIDDLE  ALT=\"log%285%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17082 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=17082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C+k%29 ALIGN=MIDDLE  ALT=\"log%28x%2C+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C+x%29 ALIGN=MIDDLE  ALT=\"log%285%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 1/2\r<BR>\n" );
document.write( "\n" );
document.write( "Note:In this problem the variable x can be assigned any positive value since <BR>\n" );
document.write( "x is not going to feature in the final answer as you may see in the following steps \r<BR>\n" );
document.write( "\n" );
document.write( "log[x](k).log[5](x) = 5/2  ----(1)<BR>\n" );
document.write( "That is log[5](k) = 5/2    (using log[b](a)Xlog[c](b) = log[c](a)   ---(*))<BR>\n" );
document.write( "This implies  k= (5)^(5/2)  <BR>\n" );
document.write( "(using definition log[b](N)=p implies and is implied by N = b^p <BR>\n" );
document.write( "where N is a strictly positive number)<BR>\n" );
document.write( "k= (5^2)X sqrt5<BR>\n" );
document.write( "k = 25sqrt5<BR>\n" );
document.write( "Answer: k= 25 times(root5)\r<BR>\n" );
document.write( "\n" );
document.write( "Verification: k= (5)^(5/2)   in <BR>\n" );
document.write( "log[x](k).log[5](x) = 5/2  ----(1)<BR>\n" );
document.write( "LHS = log[x](k).log[5](x)<BR>\n" );
document.write( "={log[x][(5)^(5/2)]}.log[5](x) <BR>\n" );
document.write( "={(5/2)log[x](5)} [log[5](x)] <BR>\n" );
document.write( "=(5/2){log[x](5)X log[5](x)}<BR>\n" );
document.write( "=(5/2)X1  {since log[b](a)=1/log[a](b) implying log[b](a)Xlog[a](b) = 1)<BR>\n" );
document.write( "=5/2 = RHS \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Detailed explanation:<BR>\n" );
document.write( "log[x](k).{1/log[x](5)} = 5/2  (using log[b](a) = 1/log[a](b) )<BR>\n" );
document.write( "log[x](k)/log[x](5) = 5/2<BR>\n" );
document.write( "That is log[5](k) = 5/2<BR>\n" );
document.write( "(using change of base rule: log[5](k) = log[x](k)/log[x](5)(the new base is x)<BR>\n" );
document.write( "This implies  k= (5)^(5/2)  <BR>\n" );
document.write( "(using definition log[b](N)=p implies and is implied by N = b^p <BR>\n" );
document.write( "where N is a strictly positive number)<BR>\n" );
document.write( "That is  k=  (5^5)^(1/2)  (using (a)^(mn) = (a^m)^n )(here a = 5, m= 5,n= 1/2)<BR>\n" );
document.write( "That is k= [5^(4+1)]^(1/2)<BR>\n" );
document.write( "k = (5^4X5^1)^(1/2)  (using a^(m+n) = a^mXa^n)<BR>\n" );
document.write( "k = (5^4)^(1/2) X (5^1)^(1/2)   (using (ab)^m= a^mXb^m )<BR>\n" );
document.write( "k = 5^[4X(1/2)]X sqrt5<BR>\n" );
document.write( "k= (5^2)sqrt5<BR>\n" );
document.write( "k = (25)times sqrt5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );