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You can put this solution on YOUR website!
log(X-7)+log(X)= log(2)+log(X+11)
\n" ); document.write( "Subtract log(2)+log(X+11) from both sides:
\n" ); document.write( "-log(2)+log(X-7)+log(X)-log(X+11) = 0 We can rewrite the left side:
\n" ); document.write( "log(1/2)+log(X-7)+log(X)+log(1/(X+11))= 0 Simplify:
\n" ); document.write( "log((X (X-7))/(2 (X+11)))= 0
\n" ); document.write( "Cancel logarithms by taking exp of both sides:
\n" ); document.write( "(X(X-7))/(2(X+11))= 1
\n" ); document.write( "Multiply both sides by 2(X+11):
\n" ); document.write( "X(X-7)= 2(X+11)
\n" ); document.write( "Expand out terms of the left:
\n" ); document.write( "X^2-7X = 2(X+11)
\n" ); document.write( "Expand out terms of the right:
\n" ); document.write( "X^2-7X = 2X+22
\n" ); document.write( "Subtract 2X+22 from both sides:
\n" ); document.write( "X^2-9X-22 = 0
\n" ); document.write( "Factor the left:
\n" ); document.write( "(X-11) (X+2) = 0
\n" ); document.write( "Split into two equations:
\n" ); document.write( "X-11= 0 or X+2= 0
\n" ); document.write( "X= 11 or X= -2
\n" ); document.write( "Plug each of these numbers into your equation to see which one makes the equation true. I did, and your answer is:
\n" ); document.write( "X = 11 \n" ); document.write( "