Question

How do you solve `log(5x-6) = 2log x`?

Answer 1

`x=2` or `x=3`

Explanation:

Note that
`color(white)("XXX") 2log(x)=log(x^2)`

So
`color(white)("XXX")log(5x-6)=2log(x)`
is equivalent to
`color(white)("XXX")log(5x-6)=log(x^2)`

which implies
`color(white)("XXX")5x-6=x^2`

`color(white)("XXX")x^2-5x+6=0`

`color(white)("XXX")(x-2)(x-3)=0`

So either
`color(white)("XXX")(x-2)=0color(white)("XX")rarrcolor(white)("XX")x=2`
or
`color(white)("XXX")(x-3)=0color(white)("xx")rarrcolor(white)("XX")x=3`