document.write( "Question 1080342: (9^x)^2=81*9^x+3 \n" ); document.write( "

Algebra.Com's Answer #694503 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"u=9%5Ex\"$ , then
\n" ); document.write( " $\"u%5E2=81u%2B3\"$
\n" ); document.write( " $\"u%5E2-81u=3\"$
\n" ); document.write( " $\"u%5E2-81u%2B%2881%2F2%29%5E2=3%2B%2881%2F2%29%5E2\"$
\n" ); document.write( " $\"%28u-81%2F2%29%5E2=12%2F4%2B6561%2F4\"$
\n" ); document.write( " $\"%28u-81%2F2%29%5E2=6573%2F4\"$
\n" ); document.write( " $\"u-81%2F2=0+%2B-+sqrt%286573%29%2F2\"$
\n" ); document.write( " $\"u=81%2F2+%2B-+sqrt%286573%29%2F2\"$
\n" ); document.write( " $\"9%5Ex=81%2F2+%2B-+sqrt%286573%29%2F2\"$
\n" ); document.write( "Only positive solutions make sense here,
\n" ); document.write( " $\"9%5Ex=81%2F2+%2B+sqrt%286573%29%2F2\"$
\n" ); document.write( " $\"x=log%289%2C%2881%2F2+%2B+sqrt%286573%29%2F2%29%29\"$
\n" ); document.write( " $\"highlight%28x=log%28%2881%2F2+%2B+sqrt%286573%29%2F2%29%29%2Flog%28%289%29%29%29\"$ \n" ); document.write( "

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