document.write( "Question 1166083: Log(10+9x)-log(11-x)=2 \n" ); document.write( "
Algebra.Com's Answer #790552 by Theo(13342)\"\" \"About 
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your equation is log(10 + 9x) - log(11 - x) = 2
\n" ); document.write( "since log(a) - log(b) is equal to log(a/b), you get:
\n" ); document.write( "log( (10+9x)/(11-x) ) = 2
\n" ); document.write( "since log(a) = b if and only if 10^b = a, you get:
\n" ); document.write( "10^2 = (10+9x)/(11-x)
\n" ); document.write( "simplify 10^2 and multiply both sides of the equaion by (11-x) to get:
\n" ); document.write( "100 * (11-x) = 10+9x
\n" ); document.write( "simplify to get 1100 - 100x = 10 + 9x
\n" ); document.write( "subtract 10 from both sides of this equation and add 100x to boh sides of this equation to get:
\n" ); document.write( "1090 = 109x
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 1090/109 = 10\r
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\n" ); document.write( "\n" ); document.write( "your solution is x = 10\r
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\n" ); document.write( "\n" ); document.write( "when x = 10, log(10 + 9x) - log(11 - x) = 2 becomes:
\n" ); document.write( "log(10 + 90) = log(11 - 10) which becomes:
\n" ); document.write( "log(100) - log(1) = 2
\n" ); document.write( "log(100) is equal to 2 and log(1) is equal to 0, so your equation becomes:
\n" ); document.write( "2 - 0 = 2 which becomes 2 = 2, confirming your solution is good.\r
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