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2-log-x-2-log-x-4-2-0-Determine-the-domain-of-x-and-find-the-value-of-x-

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Question Number 4477 by love math last updated on 30/Jan/16
2 log (x−2)+log (x−4)^2 =0 Determine the domain of x and find the value of x.
2log(x−2)+log(x−4)2=0Determinethedomainofxandfindthevalueofx.
Answered by Rasheed Soomro last updated on 30/Jan/16
2 log (x−2)+log (x−4)^2 =0 2log(x−2)=−log(x−4)^2 log(x−2)^2 =log(x−4)^(−2) (x−2)^2 =(x−4)^(−2) (x−2)^2 =((1/(x−4)))^2 x−2=±(1/(x−4)) (x−2)(x−4)=±1 x^2 −6x+8−1=0 ∣ x^2 −6x+8+1=0 x^2 −6x+7=0 ∣ x^2 −6x+9=0 x=((−(−6)±(√((−6)^2 −4(1)(7))))/2) ∣ (x−3)^2 =0 x=((6±(√8))/2)=3±(√2) ∣ x=3 Domain of equation :{3,3±(√2)}
2log(x−2)+log(x−4)2=02log(x−2)=−log(x−4)2log(x−2)2=log(x−4)−2(x−2)2=(x−4)−2(x−2)2=(1x−4)2x−2=±1x−4(x−2)(x−4)=±1x2−6x+8−1=0∣x2−6x+8+1=0x2−6x+7=0∣x2−6x+9=0x=−(−6)±(−6)2−4(1)(7)2∣(x−3)2=0x=6±82=3±2∣x=3Domainofequation:{3,3±2}

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