document.write( "Question 691108: Find the exact value for the solution of the equation.
\n" ); document.write( "log((x^2)+4)-log(x+2)=2+log(x-2)
\n" ); document.write( "I have the answer in the back of my book and it says the answer is: (2/3)*(sqrt(101/11))=~2.02
\n" ); document.write( "But every way I've tried didnt work. Please help! and thank you! \n" ); document.write( "
Algebra.Com's Answer #426575 by ankor@dixie-net.com(22740)\"\" \"About 
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exact value for the solution of the equation.
\n" ); document.write( "log(x^2+4)-log(x+2) = 2+log(x-2)
\n" ); document.write( "subtracting indicates divide so we can write it
\n" ); document.write( "\"log%28%28%28x%5E2%2B4%29%2F%28x%2B2%29%29%29\" = 2 + log(x-2)
\n" ); document.write( "Subtract log(x-2) from both sides
\n" ); document.write( "\"log%28%28%28x%5E2%2B4%29%2F%28x%2B2%29%29%29\" - log(x-2) = 2
\n" ); document.write( "which we can combine
\n" ); document.write( "\"log%28%28%28x%5E2%2B4%29%2F%28%28x%2B2%29%28x-2%29%29%29%29\" = 2
\n" ); document.write( "which is
\n" ); document.write( "\"log%28%28%28x%5E2%2B4%29%2F%28x%5E2-4%29%29%29\" = 2
\n" ); document.write( "find the antilog (10^x) of both sides (10^2 = 100)
\n" ); document.write( "\"%28%28x%5E2%2B4%29%2F%28x%5E2-4%29%29\" = 100
\n" ); document.write( "multiply both sides by x^2-4
\n" ); document.write( "\"x%5E2+%2B+4+=+100%28x%5E2-4%29\"
\n" ); document.write( "\"x%5E2+%2B+4+=+100x%5E2-400\"
\n" ); document.write( "combine like terms
\n" ); document.write( "0 = 100x^2 - x^2 - 400 - 4
\n" ); document.write( "99x^2 - 404 = 0
\n" ); document.write( "99x^2 = 404
\n" ); document.write( "x^2 = \"404%2F99\"
\n" ); document.write( "x = \"sqrt%28404%2F99%29\"
\n" ); document.write( "x = \"sqrt%28%284%2A101%29%2F%289%2A11%29%29\"
\n" ); document.write( "Extract the square roots of the perfect squares
\n" ); document.write( "x =\"2%2F3\"*\"sqrt%28101%2F11%29\"
\n" ); document.write( "x ~ 2.02\r
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