Question

Please help me I'm desperate.

Answer 1

`\log (4x - 1) - \log (x + 2) = \log x`

`\log ( (4x - 1)/(x + 2) ) = \log x`

`(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`

Answer 2

`D:4x-1>0 \wedge x+2 >0 \wedge x>0\\ D:4x>1 \wedge x>-2 \wedge x>0\\ D:x>(1)/(4) \wedge x>0\\ D:x>(1)/(4)\\\\ \log(4x-1)-\log(x+2)=\log x\\ \log(4x-1)/(x+2)=\log x\\ (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}`