SOLUTION: solve the equation log[2](x-5)+log[2](x-11)=4

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Question 604678: solve the equation log[2](x-5)+log[2](x-11)=4
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
log[2](x-5)+log[2](x-11)=4
log[2]((x-5)*(x-11))=4
%28x-5%29%2A%28x-11%29+=+2%5E4
x%5E2+-+11x+-+5x+%2B+55+=+16
x%5E2+-+16x+%2B+55+=+16
x%5E2+-+16x+%2B+55+-+16=0
x%5E2+-+16x+%2B+39=0
(x - 13)*(x - 3) = 0
x - 13 = 0 or x - 3 = 0
x = 13 or x = 3

if we substitute those x values in the logarithm function, x = 3 will make a negative number within the log function:
log[2](x-5)=log[2](3-5) = log[2](-2)
the number in the log function can't be a negative number, so the solution is:
x = 13