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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

 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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neela | High School Teacher | (Level 3) Valedictorian

Posted on

log2 (x+5) +log2 (x+2) = log (x+6)

Solution:

loga+log b = logab .

Therefore,

log2 (+5)+log2(x+2) = log2 (x+6)

log2 (x+5)(x+2) = log2 (x+6). Takinh antilog to base 2,

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

x^2+6x+10 = x+6

x^2+7x+10-x-6 = 0

x^2+5x+4 = 0

(x+1)(x+4) = 0

x+1 = 0 , x+4 = 0.

x=-1 or x=-4

 

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