express a single logarithm

1/3 log(b, x+3) log(b, y-4) log(b, x)

Are you sure these logs weren't added ?

then we could do something, but the way it sits, I see no simplification

To express the given expression as a single logarithm, we can use the properties of logarithms. Specifically, we can use the product rule and the quotient rule to combine the individual logarithms into a single one.

Let's start by using the product rule, which states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. In this case, we have:

1/3 log(b, x+3) + log(b, y-4) + log(b, x)

Next, let's use the quotient rule, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. However, we don't have a quotient in this expression, so we need to modify it slightly to use the quotient rule. We can rewrite the expression as:

1/3 log(b, x+3) + log(b, y-4) + log(b, x) - log(b, 1)

Since log(b, 1) is equal to 0 for any base b, it doesn't change the value of the expression. Therefore, we can remove it, leading to:

1/3 log(b, x+3) + log(b, y-4) + log(b, x)

Now we have successfully expressed the given expression as a single logarithm.