Question

How do you solve `log(x) + log(2x + 1) = 1`?

Answer 1

`color(white)xxx_1=2`
`color(white)xxx_2=-5/2`

Explanation:

`color(white)xxlogx+log(2x+1)=1`

`=>logx(2x+1)=1`
`=>2x^2+x=10`
`=>2x^2+x-10=0`

`color(white)xxDelta=81`
`=>x_(1,2)=(-1+-9)/4`

`=>x_1=2`
`=>x_2=-5/2`