4log(x)-10log(y)+2log(z)=

Question

Write as logarithm of single expression

Answer 1

The answer above looks like log is only for the numerator.

It will be better if we write it as

log [ x⁴ z²/ y¹⁰]

Answer 2

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)