1. ## expand logrithmic expression

How do I expand this:
$log_4\frac{2\sqrt[3]{x-5}}y^7$

Am I on the right path?:
$log_4(2(x-5))^{\frac{1}{3}}-y^7$

2. Hello,

A little typo :

$
log_4\frac{2\sqrt[3]{x-5}}{y^7}
$

$log_4(2(x-5))^{\frac{1}{3}}-y^7$
Not really, you forgot something important and you did a mistake in the brackets.

It's actually $\log_4(2(x-5)^{\frac{1}{3}})-\log_4(y^7)$

But the idea was good

3. From there, what should my next step be?

4. Use the properties of logarithm :

$\log(xy)=\log(x)+\log(y)$

$\log(a^b)=b\log(a)$

Do you need more indication ?

5. $log_4(2)+{\frac{1}{3}}log_4(x-5)-7log_4(y)$?

Are there any more steps? I think that is all I can expand it to.

6. I think this is perfect ^^

One more thing :

$2=4^{1/2}$

Since $\log_4(4)=1$, do you think you can go further ?