Question

How do you simplify `log x + log (x^2 - 196) - log 2 - log (x - 14)`?

Answer 1

`log((x*(x^2-16))/(2*(x-14)))`

Explanation:

We write
`log(x)+log(x^2-16)-(log(2)+log(x-14))`
and this is
`log(x*(x^2-16))-log(2(x-14))`
This is
`log((x(x^2-16))/(2*(x-14)))`
We have used that
`log(ab)=log(a)+log(b)`
`log(a/b)=log(a)-log(b)`
for `a,b>0`