document.write( "Question 21665: log base3 x +log base3 (x-4) +16=18 \n" ); document.write( "
Algebra.Com's Answer #10450 by Earlsdon(6294)\"\" \"About 
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Solve for x:
\n" ); document.write( "log\"3\"(x)+log\"3\"(x-4)+16 = 18 Subtract 16 from both sides.
\n" ); document.write( "log\"3\"(x)+log\"3\"(x-4) = 2 Apply the product rule for logarithms:Log\"b\"M+log\"b\"N = log\"b\"(MN)
\n" ); document.write( "log\"3\"(x)+log\"3\"(x-4) = log\"3\"(x^2-4x) = 2 Rewrite in exponential form:
\n" ); document.write( "log\"b\"x = y means \"b%5Ey+=+x\" so:
\n" ); document.write( "log\"3\"(x^2-4x) = 2 means \"3%5E2+=+%28x%5E2-4x%29\" Subtract 3^2 = 9 from both sides.
\n" ); document.write( "\"x%5E2-4x-9+=+0\" Solve using the quadratic formula: \"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"
\n" ); document.write( "\"x+=+%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%281%29%28-9%29%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%284%2B-sqrt%2852%29%29%2F2\" = \"%284%2B-sqrt%284%2A13%29%29%2F2\"
\n" ); document.write( "\"x+=+2%2B-sqrt%2813%29\"\r
\n" ); document.write( "\n" ); document.write( "The roots are:
\n" ); document.write( "\"x+=+2%2Bsqrt%2813%29\"
\n" ); document.write( "\"x+=+2-sqrt%2813%29\"
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