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Write as logarithm of single expression

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2 Answers

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)