document.write( "Question 701297: I think this is the right section..
\n" ); document.write( "Solve 9^n –(6 × 3^n)– 27 = 0 and explain why it has only one real solution.
\n" ); document.write( "Hint: let 3^n = x\r
\n" ); document.write( "\n" ); document.write( "Can someone please solve this for me?\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #432353 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
If 3^n = x , then x^2 = (3^n)^2 which means x^2 = (3^2)^n and that x^2 = 9^n\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "9^n –(6 × 3^n)– 27 = 0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "would turn into\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x^2 - 6x - 27 = 0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This has at most 2 solutions. It turns out that the two solutions are x = 9 or x = -3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "However, since x = 3^n and 3^n is always positive (for any value of n), saying x = -3 or 3^n = -3 is impossible because there are no values of n that satisfy that equation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So there is only one solution, namely x = 9. Since x = 3^n, the solution for n is n = 2 \n" ); document.write( "

\n" );