Write as logarithm of single expression
The answer above looks like log is only for the numerator.
It will be better if we write it as
log [ x4 z2/ y10]
b log(a) is the same as log (a)b.
log (a) + log (b) is the same as log (ab). Similarly, log (a) - log (b) = log (a/b)
Using the first rule, we can simplify the expression:
4 log(x) - 10 log(y) + 2 log (z) = log (x)4 - log (y)10 + log (z)2
Now, using the second and third rules, we can simplify to a single expression:
log (x)4 - log (y)10 + log (z)2 = log (x4z2)/(y10)