document.write( "Question 851467: SOLVE FOR THE VAULE OF X: 27^X=9^X+2 \n" ); document.write( "
Algebra.Com's Answer #512769 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the equation, as far as i can tell is:\r
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\n" ); document.write( "\n" ); document.write( "27^x = 9^(x+2)\r
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\n" ); document.write( "\n" ); document.write( "if so, then the answer is x = 4 which has been derived as shown below:\r
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\n" ); document.write( "\n" ); document.write( "start with:
\n" ); document.write( "27^x = 9^(x+2)
\n" ); document.write( "take the log of both sides of the equation to get:
\n" ); document.write( "log(27^x) = log(9^(x+2))
\n" ); document.write( "use the property of log(a^x) = x*log(a) to get:
\n" ); document.write( "x*log(27) = (x+2)*log(9)
\n" ); document.write( "simplify by removing parentheses to get:
\n" ); document.write( "x*log(27) = x*log(9) + 2*log(9)
\n" ); document.write( "subtract x*log(9) from both sides of the equation to get:
\n" ); document.write( "x*log(27) - x*log(9) = 2*log(9)
\n" ); document.write( "factor out the x to get:
\n" ); document.write( "x*(log(27) - log(9)) = 2*log(9)
\n" ); document.write( "divide both sides of the equation by (log(27)-log(9)) to get:
\n" ); document.write( "x = 2*log(9) / (log(27) - log(9))
\n" ); document.write( "solve for x by taking the log of 9 and log of 27 and evaluating the equation to get:
\n" ); document.write( "x = 4
\n" ); document.write( "replace x in the original equation to get:
\n" ); document.write( "27^x = 9^(x+2) becomes 27^4 = 9^6 which becomes 531441 = 531441
\n" ); document.write( "this confirms the solution is good.\r
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