Question

How do you write as a single log for `log_460 - log_44 + log_4x`?

Answer 1

I think you intended `log_4 60 - log_4 4 + log_4 x`.

If so, then using the basic properties of logs this simplifies to:

`log_4 15x`

Explanation:

In general, `log_a b + log_a c = log_a bc`

and `log_a b - log_a c = log_a (b/c)`

So:

`log_4 60 - log_4 4 + log_4 x`

`=log_4 (60/4) + log_4 x`

`=log_4 15 + log_4 x`

`=log_4 15x`