document.write( "Question 448288: Log 2 (3x-2)- Log 2 (x-5)=4 \n" ); document.write( "
Algebra.Com's Answer #309015 by lwsshak3(11628)\"\" \"About 
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Log 2 (3x-2)- Log 2 (x-5)=4
\n" ); document.write( "..
\n" ); document.write( "Log 2 (3x-2)- Log 2 (x-5)=4
\n" ); document.write( "log2 (3x-2)/(x-5)=4 (division rule for logs)
\n" ); document.write( "convert to exponential form (base(2) raised to log of number(4) is equal to number((3x-2)/(x-5)
\n" ); document.write( "2^4=(3x-2)/(x-5)
\n" ); document.write( "16=3x^2-17x+10
\n" ); document.write( "3x^2-17x-6=0
\n" ); document.write( "solve by quadratic formula below:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "..
\n" ); document.write( "a=3, b=-17, c=-6
\n" ); document.write( "x=[-(-17)ħsqrt((-17)^2-4*3*-6)]/2*3
\n" ); document.write( "x=[17ħsqrt(361)]6
\n" ); document.write( "x=(17ħ19)/6
\n" ); document.write( "x=36/6=6
\n" ); document.write( "or
\n" ); document.write( "x=-2/6=-1/3 (reject, (x-5)>0)
\n" ); document.write( "Check: with x=6
\n" ); document.write( "log2(3*6-2)-log2(6-5)
\n" ); document.write( "log2(16)-log2(1)=4-0=4 \n" ); document.write( "
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