log(2x+3)+log(2x-3)=log55. what is the value of x
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Answer:
The value of x is = 4
Step-by-step explanation:
The given equation is,
log(2x+3) + log(2x-3) = log55
Solving the given equation,
=> log((2x+3) ×(2x-3)) = log55 [ as, logab = loga + logb]
= log(4x^2-3^2) = log55 [ as, (a+b) ×(a-b) = a^2-b^2]
=> log(4x^2 -9) = log55
=> 4x^2-9 = 55
=> 4x^2 = 55+9 = 64
=> 4x^2 = 64
=> x^2 = 64/4 = 16
=> x = √16 = 4
So, the value of x = 4
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