document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174281>Question 1174281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/2 log(base3) of M + 3log(bases)ofN=1,express M in terms of N. </SPAN>\n" );
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document.write( "log rules:<BR>\n" );
document.write( "(1) log(ab) = log(a)+log(b)<BR>\n" );
document.write( "(2) log(a^n) = n*log(a)<br><BR>\n" );
document.write( "1/2 log(base 3) of M = log(base 3) of M^(1/2)  (rule (1))<BR>\n" );
document.write( "3log(base 3) of N = log(base 3) of N^3  (rule (1))<br><BR>\n" );
document.write( "log(base 3) of M^(1/2) + log(base 3) of N^3 = log(base 3) of ((M^1/2)(N^3))  (rule 2)<br><BR>\n" );
document.write( "Now the equation is<br><BR>\n" );
document.write( "log(base 3) of ((M^1/2)(N^3)) = 1<br><BR>\n" );
document.write( "Translating that to exponential form gives us<br><BR>\n" );
document.write( "(M^1/2)(N^3) = 3^1 = 3<br><BR>\n" );
document.write( "Solving for M in terms of N:<br><BR>\n" );
document.write( "{M)(N^6) = 9  (squaring both sides)<BR>\n" );
document.write( "M = 9/N^6<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );