Question

How do you solve `log (x+4)=log x + log 4`?

Answer 1

`log(x+4) = log(x) + log(4) = log(4x)`, so `x+4 = 4x`, hence `x = 4/3`

Explanation:

If `a, b > 0` then `log(a)` and `log(b)` are defined and

`log(a) + log(b) = log(ab)`

So `log(x) + log(4) = log(4x)`

So our equation becomes:

`log(x + 4) = log x + log 4 = log(4x)`

Since `log:(0, oo) -> RR` is one-one, that means:

`x+4 = 4x`

Subtract `x` from both sides to get `4 = 3x`, then divide both sides by `3` to get `x = 4/3`.