# Thread: Please help with an ln problem

1. ## Please help with an ln problem

Can anyone help with this problem?

ln(r^3s^7([7th root](r^7s^10)))

is equal to A ln r +B ln s

where A=______ and B=________

This is what I have so far:
3 ln r + 7 ln s + 7th root (r^7s^10)

I thought it should be
3 ln r + 7 ln s + 49/2 ln r + 70/2 ln s=
55/2 ln r + 84/2 ln s

but that is wrong. How do you do the 7th root?

2. Originally Posted by operaphantom2003
Can anyone help with this problem?

ln(r^3s^7([7th root](r^7s^10)))

is equal to A ln r +B ln s

where A=______ and B=________

This is what I have so far:
3 ln r + 7 ln s + 7th root (r^7s^10)

I thought it should be
3 ln r + 7 ln s + 49/2 ln r + 70/2 ln s=
55/2 ln r + 84/2 ln s

but that is wrong. How do you do the 7th root?
$\ln(r^3 s^7 \sqrt[7]{r^7 s^{10}})$

$\ln(r^3 s^7 \cdot r s^{\frac{10}{7}})$

$\ln(r^4 s^{\frac{59}{7}})$

$\ln(r^4) + \ln(s^{\frac{59}{7}})$

$4\ln{r} + \frac{59}{7}\ln{s}$