# Math Help - Expanding Log problem...

1. ## Expanding Log problem...

Expand as the sum of individual logarithms, each of whose argument is linear: $log(\frac{xy^2}{z^4})$

your help is appreciated! Thanks.

2. Originally Posted by Savior_Self
Expand as the sum of individual logarithms, each of whose argument is linear: $log(\frac{xy^2}{z^4})$

your help is appreciated! Thanks.
Using the following logarithm rules:

$log(ab) = log(a) + log(b)$
$log(\frac{a}{b})= log(a) - log(b)$
$log(a^n) = n \cdot log(a)$

I will start, see if you can finish:

$log(\frac{xy^2}{z^4}) = log(xy^2) - log(z^4) = log(xy^2) - 4log(z)$

...

3. Originally Posted by Defunkt
Using the following logarithm rules:

$log(ab) = log(a) + log(b)$
$log(\frac{a}{b})= log(a) - log(b)$
$log(a^n) = n \cdot log(a)$

I will start, see if you can finish:

$log(\frac{xy^2}{z^4}) = log(xy^2) - log(z^4) = log(xy^2) - 4log(z)$

...
so...

$log(x) + log(y^2) - 4log(z)
=
log(x) + 2log(y) - 4log(z)$

answer being...

$log(x) + 2log(y) - 4log(z)$

Look good?

4. Originally Posted by Savior_Self
so...

$log(x) + log(y^2) - 4log(z)
=
log(x) + 2log(y) - 4log(z)$

answer being...

$log(x) + 2log(y) - 4log(z)$

Look good?
Yes, that is correct.