Question

How do you expand this logarithm?

`log_(3)(z^(4)sqrtx)`

Answer 1

`4log_3 (z) + 1/2log_3(x)`

Explanation:

General Rules:
`color(white)("XXX")log_b a^c = c * log_b a`

`color(white)("XXX")log_b (a * c) = log_b + log_b c`

Answer 2

`4log_3(z)+1/2log_3(x)`.

Explanation:

By using the rule of logarithms where `log(a*b)=loga+logb`, we first get

`log_3(z^4sqrtx)`
`=log_3(z^4)+log_3(sqrtx)`
`=log_3(z^4)+log_3(x^(1//2))`

Another rule of logarithms is `log(a^b)=blog(a)`. We now use this to get

`=4log_3(z)+1/2log_3(x)`

Unless you have been asked to rewrite the "base 3" logarithms in "base 10" form, this is as much expansion as we can do.

Hope this helps!