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Sagot :
[tex]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}
[/tex]
[tex]\log (4x - 1) - \log (x + 2) = \log x[/tex]
[tex]\log ( \frac{4x - 1}{x + 2} ) = \log x[/tex]
[tex] \frac{4x - 1}{x + 2} = x[/tex]
[tex]4x - 1 = x(x + 2)[/tex]
[tex]4x - 1 = x^2 + 2x[/tex]
[tex]0 = x^2 - 2x + 1[/tex]
[tex]0 = (x - 1)^2[/tex]
⇒ [tex]x = 1[/tex]
[tex]\log ( \frac{4x - 1}{x + 2} ) = \log x[/tex]
[tex] \frac{4x - 1}{x + 2} = x[/tex]
[tex]4x - 1 = x(x + 2)[/tex]
[tex]4x - 1 = x^2 + 2x[/tex]
[tex]0 = x^2 - 2x + 1[/tex]
[tex]0 = (x - 1)^2[/tex]
⇒ [tex]x = 1[/tex]
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