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Write as logarithm of single expression

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Rini C. | Math made easyMath made easy
5.0 5.0 (527 lesson ratings) (527)

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

It will be better if we write it as

log [ x4 z2/ y10]

Kevin S. |
5.0 5.0 (4 lesson ratings) (4)

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)