document.write( "Question 808426: Solve the following exponential equation: 3^(2x) -4(3^x) + 3 = 0 \n" ); document.write( "

Algebra.Com's Answer #487007 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+3%5E%282x%29+-4%283%5Ex%29+%2B+3+=+0+\"$
\n" ); document.write( "Let's call $\"3%5Ex\"$ by a different name:
\n" ); document.write( " $\"3%5Ex=y\"$ --> $\"3%5E%282x%29=%283%5Ex%29%5E2=y%5E2\"$
\n" ); document.write( "With that change of variable, the equation becomes
\n" ); document.write( " $\"y%5E3-4y%2B3=0\"$
\n" ); document.write( "Factoring it turns into
\n" ); document.write( " $\"%28y-1%29%28y-3%29=0\"$
\n" ); document.write( "with solutions $\"y=1\"$ and $\"y=3\"$
\n" ); document.write( "Returning to the original variable $\"x\"$ ,
\n" ); document.write( " $\"y=1\"$ --> $\"3%5Ex=1\"$ --> $\"highlight%28x=0%29\"$
\n" ); document.write( "or $\"y=3\"$ --> $\"3%5Ex=3\"$ --> $\"highlight%28x=1%29\"$ \n" ); document.write( "

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