document.write( "Question 730965: LogBase4(x-2)+LogBase4(x+10)=3 \n" ); document.write( "
Algebra.Com's Answer #446957 by fcabanski(1391)\"\" \"About 
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Remember that log(base n) (x) + log(base n) (y) = log(base n) (xy)


\n" ); document.write( "LogBase4(x-2)+LogBase4(x+10)=3


\n" ); document.write( "logbase((x-2)*(x+10)) = 3


\n" ); document.write( "logbase4(x^2 + 8x -20) = 3


\n" ); document.write( "Recall that logbasen (x) = y if and only if n^y = x.


\n" ); document.write( "\"x%5E2+%2B+8x+-+20+=+4%5E3+=+64\"


\n" ); document.write( "\"x%5E2+%2B+8x+-+84+=+0\"
\n" ); document.write( "(x+14)(x-6) = 0


\n" ); document.write( "x=-14 and x=6


\n" ); document.write( "The log of a negative number is imaginary. So only x=6 works. -14 results in logbase4 (-16) + logbase4 (-4) = 3 . The log of negative numbers isn't real.
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