Question

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

Answer 1

`x=(1+sqrt(17))/4`

Explanation:

If
`color(white)("XXX")log(x)=log(2x^2-2)`
then
`color(white)("XXX")x=2x^2-2`

`rArr 2x^2-x-2=0`

Using the quadratic formula for roots: `x=(-b+-sqrt(b^2-4ac))/(2a)`
gives
`color(white)("XXX")x=(1+-sqrt(17))/4`

Since the argument of `log` can not be negative,
we can eliminate `(1-sqrt(17))/4` as extraneous,
leaving only the answer above.