Calculate x from: Log (x + 4) + log (3x + 2) = log 100 - 2log 2

x = 1

Step-by-step 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.

step-by-step explanation:

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step-by-step explanation: