Verified Answer :

konrad509

\(D:4x-1>0 \wedge x+2 >0 \wedge x>0\\ D:4x>1 \wedge x>-2 \wedge x>0\\ D:x>\frac{1}{4} \wedge x>0\\ D:x>\frac{1}{4}\\\\ \log(4x-1)-\log(x+2)=\log x\\ \log\frac{4x-1}{x+2}=\log x\\ \frac{4x-1}{x+2}=x\\ x(x+2)=4x-1\\ x^2+2x=4x-1\\ x^2-2x+1=0\\ (x-1)^2=0\\ \boxed{x=1}\)

superkoopasirf

\(\log (4x - 1) - \log (x + 2) = \log x\)
\(\log ( \frac{4x - 1}{x + 2} ) = \log x\)
\(\frac{4x - 1}{x + 2} = x\)
\(4x - 1 = x(x + 2)\)
\(4x - 1 = x^2 + 2x\)
\(0 = x^2 - 2x + 1\)
\(0 = (x - 1)^2\)
⇒ \(x = 1\)

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