SOLUTION: Question goes like this.... Solve Equation. 2log2 (x+6)

SOLUTION: Question goes like this.... Solve Equation. 2log2 (x+6) - log2 16 = 2

Question 35332: Question goes like this....
Solve Equation.
2log2 (x+6) - log2 16 = 2
Answer by narayaba(40) (Show Source): You can put this solution on YOUR website!
2log2 (x+6) - log2 16 =2
m*loga (b) = loga (b^m)
similarly
2log2 (x+6) = log2 (x+6)^2
2log2 (x+6) - log2 16 =2 can we written as log2 (x+6)^2 - log2 16 =2
loga b -log a c = loga (b/c)
log2 (x+6)^2 - log2 16 =2 is same as log2 (x+6)^2/16 = 2
log2 2 =1
log2 (x+6)^2/16 = 2*log2
log2 (x+6)^2/16 = log2 4
log on right and left side is to the same base
therefore
(x+6)^2/16 = 4
(x+6)^2 = 64
(a+b)^2 = a^2 + b^2 +2*a*b
x^2 + 12*x +36 = 64
x^2 + 12*x -28 =0
factorixing x^2 + 12*x -28 =0 as (x+14)(x-2)=0
x = -14 or x =2

log of negative number is not posible hence x = 2

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