document.write( "Question 104905: Hi there, \r
\n" ); document.write( "\n" ); document.write( "I'm completely stumped. I need to solve for X:\r
\n" ); document.write( "\n" ); document.write( "(9^(2x))*(27^(x-3))=1/9\r
\n" ); document.write( "\n" ); document.write( "I graphed it, and know that the answer SHOULD be -11, but I need to see HOW to do the problem.\r
\n" ); document.write( "\n" ); document.write( "Thank you,\r
\n" ); document.write( "\n" ); document.write( "Brad Easler \n" ); document.write( "

Algebra.Com's Answer #76359 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9\"$
\n" ); document.write( "Use the exponentiation rules
\n" ); document.write( " $\"%28x%5Em%29%5En=x%5E%28m%2An%29\"$
\n" ); document.write( " $\"%28x%5Em%29%2A%28x%5En%29=x%2A%28m%2Bn%29\"$
\n" ); document.write( "Let's start.
\n" ); document.write( " $\"%28%283%5E2%29%5E%282x%29%2A%283%5E3%29%5E%28x-3%29%29=3%5E%28-2%29+\"$ Convert to the same base, 3.
\n" ); document.write( " $\"3%5E%284x%29%2A%283%5E%283%28x-3%29%29%29=3%5E%28-2%29+\"$ Use the rules.
\n" ); document.write( " $\"3%5E%284x%2B%283%28x-3%29%29%29=3%5E%28-2%29+\"$ Simplify.
\n" ); document.write( " $\"4x%2B3%28x-3%29=-2\"$ Inverse function.
\n" ); document.write( " $\"4x%2B3x-9=-2\"$ Distribute.
\n" ); document.write( " $\"7x-9=-2\"$ Additive inverse.
\n" ); document.write( " $\"7x=7\"$ Multiplicative inverse.
\n" ); document.write( " $\"x=1\"$
\n" ); document.write( "Verify the solution.
\n" ); document.write( " $\"%289%5E%282x%29%29%2A%2827%5E%28x-3%29%29=1%2F9\"$
\n" ); document.write( " $\"%289%5E%282%29%29%2A%2827%5E%281-3%29%29=1%2F9\"$
\n" ); document.write( " $\"%2881%2F729%29=1%2F9\"$
\n" ); document.write( " $\"%281%2F9%29=1%2F9\"$
\n" ); document.write( "Good answer. \n" ); document.write( "

\n" );