document.write( "Question 262500: pls help...if 9^x=27^y and 8^y=16^z, then what is the value of x:y:z?? thank u in advance \n" ); document.write( "
Algebra.Com's Answer #193398 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
pls help...if 9^x=27^y and 8^y=16^z, then what is the value of x:y:z
\n" ); document.write( "

\n" );
document.write( "\"9%5Ex=27%5Ey\"
\n" );
document.write( "\"%283%5E2%29%5Ex=%283%5E3%29%5Ey\"
\n" );
document.write( "\"3%5E%282x%29=3%5E%283y%29\"
\n" );
document.write( "The bases are equal, positive, and not 1, so
\n" );
document.write( "the exponents are equal
\n" );
document.write( "\"2x=3y\"\r
\n" );
document.write( "\n" );
document.write( "Divide both sides by 2y\r
\n" );
document.write( "\n" );
document.write( "\"x%2Fy=3%2F2\"\r
\n" );
document.write( "\n" );
document.write( "\"%22x%3Ay%22=%223%3A2%22\"\r
\n" );
document.write( "\n" );
document.write( "-------------------\r
\n" );
document.write( "\n" );
document.write( "\"8%5Ey=16%5Ez\"
\n" );
document.write( "\"%282%5E3%29%5Ey=%282%5E4%29%5Ez\"
\n" );
document.write( "\"2%5E%283y%29=2%5E%284z%29\"
\n" );
document.write( "The bases are equal, positive, and not 1, so
\n" );
document.write( "the exponents are equal
\n" );
document.write( "\"3y=4z\"\r
\n" );
document.write( "\n" );
document.write( "Divide both sides by 3z\r
\n" );
document.write( "\n" );
document.write( "\"y%2Fz=4%2F3\"\r
\n" );
document.write( "\n" );
document.write( "\"%22y%3Az%22=%224%3A3%22\"\r
\n" );
document.write( "\n" );
document.write( "\"%22x%3Ay%22=%223%3A2%22\" and \"%22y%3Az%22=%224%3A3%22\"\r
\n" );
document.write( "\n" );
document.write( "y corresponds to 2 in the first ratio
\n" );
document.write( "but y corresponds to 4 in the second ratio.
\n" );
document.write( "The least common multiple is 4, so change
\n" );
document.write( "the first ratio to \r
\n" );
document.write( "\n" );
document.write( "\"%22x%3Ay%22=%226%3A4%22\" \r
\n" );
document.write( "\n" );
document.write( "and we now have\r
\n" );
document.write( "\n" );
document.write( "\"%22x%3Ay%22=%226%3A4%22\" and \"%22y%3Az%22=%224%3A3%22\"\r
\n" );
document.write( "\n" );
document.write( "so that y corresponds to the same number, 4,
\n" );
document.write( "in both ratios, and now we can write:\r
\n" );
document.write( "\n" );
document.write( "\"%22x%3Ay%3Az%22=%226%3A4%3A3%22\"\r
\n" );
document.write( "\n" );
document.write( "Edwin
 \n" );
document.write( "
\n" );