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 [ x^{4} z^{2}/ y^{10}]

Write as logarithm of single expression

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

It will be better if we write it as

log [ x^{4} z^{2}/ y^{10}]

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 (x**^{4}**z**^{2}**)/(y ^{10}**