Question

How do you solve `Log(3x+2)-log(2x-1)=log 2`?

Answer 1

`x=4`

Explanation:

In general `log(a/b) = log(a) - log(b)`

Therefore
`color(white)("XXX")log(3x+2)- log(2x-1) = log((3x+2)/(2x-2))`

So
`color(white)("XXX")log(3x+2)-log(2x+1) = log(2)`

`rArrcolor(white)("XXX")log((3x+2)/(2x-1))= log(2)`

`rArrcolor(white)("XXX")(3x+2)/(2x-1)=2`

`rArrcolor(white)("XXX")3x+2 = 4x-2`

`rArrcolor(white)("XXX")x=4`