log 2 (x+5) + log 2 (x+2) = log 2 (x+6)

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 log 2 (x+5) + log 2 (x+2) = log 2 (x+6)

We know that log x + log y = log x*y

==> log 2 (x+5)(x+2) = log 2 (x+6)

We know that if log x = log y ==> x=y

==> (x+5)(x+2) = (x+6)

Open brackets:

==> x^2 +...

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 log 2 (x+5) + log 2 (x+2) = log 2 (x+6)

We know that log x + log y = log x*y

==> log 2 (x+5)(x+2) = log 2 (x+6)

We know that if log x = log y ==> x=y

==> (x+5)(x+2) = (x+6)

Open brackets:

==> x^2 + 7x + 10 = x+6

==> X^2 + 6X + 4 =0

==> x =[ -6 + sqrt(36-16)]/2\

           = [-6 + sqrt(20)] / 2

           = [-6 + 2sqrt(5)]/2

            = -3 + sqrt(5)

==> the answer is x = -3 + sqrt(5)

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