Answer: x = 1
Explanation:
Given that
Log (x + 4) + log (3x + 2) = log 100 - 2log 2
Log (x + 4) + log (3x + 2) = log 100 - log2^2
Log (x + 4) + log (3x + 2) = log 100 - log4
According to the laws of logarithms,
LogA + logB = log AB
Also,
Log A - logB = log A/B
Apply the law to left hand side and the right hand side of the equation
Log (x+4)(3x+2) = log(100/4)
Open the bracket in the left hand side
Log(3x^2 + 2x +12x + 8) = log25
Log(3x^2 + 14x + 8) = log25
The two log will cancel out
3x^2 + 14x + 8 = 25
3x^2 + 14x + 8 - 25 = 0
3x^2 + 14x - 17 = 0
Factorise the above equation
3x^2 - 3x + 17x - 17 = 0
3x( x - 1 ) + 17( x - 1 ) = 0
3x + 17 = 0
3x = - 17
X = -17/3
Or
X - 1 = 0
X = 1
Therefore, x = -17 or 1
Substituting 1 back into the equation give the solution to the equation. While -17 does not.