document.write( "Question 313118: 3^(2x-1) = 10*(3^x)-3. \"How to solve x?\" thank you \n" ); document.write( "

Algebra.Com's Answer #223923 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3%5E%282x-1%29+=+10%2A%283%5Ex%29-3\"$
\n" ); document.write( " $\"3%5E%282x%29%2F3=10%2A3%5E%28x%29-3\"$
\n" ); document.write( "Substitute $\"u=3%5Ex\"$ , then $\"u%5E2=3%5E%282x%29\"$
\n" ); document.write( " $\"u%5E2%2F3=10%2Au-3\"$
\n" ); document.write( " $\"u%5E2=30u-9\"$
\n" ); document.write( " $\"u%5E2-30u%2B9=0\"$
\n" ); document.write( "Use the quadratic formula,
\n" ); document.write( " $\"u+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"u+=+%2830+%2B-+sqrt%28+900-36+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"u+=+%2830+%2B-+sqrt%28+864%29%29%2F%282%29+\"$
\n" ); document.write( " $\"u+=+%2830+%2B-+12sqrt%28+6%29%29%2F%282%29+\"$
\n" ); document.write( " $\"u+=+15+%2B-+6sqrt%28+6%29+\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"u1=15%2B6sqrt%286%29\"$
\n" ); document.write( " $\"3%5E%28x%29=15%2B6sqrt%286%29\"$
\n" ); document.write( " $\"x=log%283%2C%2815%2B6sqrt%286%29%29%29\"$
\n" ); document.write( " $\"x=log%2810%2C%2815%2B6sqrt%286%29%29%29%2Flog%2810%2C%283%29%29+\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( " $\"u2=15-6sqrt%286%29\"$
\n" ); document.write( " $\"3%5E%28x%29=15-6sqrt%286%29\"$
\n" ); document.write( " $\"x=log%283%2C%2815-6sqrt%286%29%29%29\"$
\n" ); document.write( " $\"x=log%2810%2C%2815-6sqrt%286%29%29%29%2Flog%2810%2C%283%29%29+\"$
\n" ); document.write( " \n" ); document.write( "

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