Answer:
C ![4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)](https://tex.z-dn.net/?f=4%5Clog_w%28x%5E2-6%29-%5Cdfrac%7B1%7D%7B3%7D%5Clog_w%28x%5E2%2B8%29)
Step-by-step explanation:
First use the property of logarithms
![\log _ab-\log_ac=\log_a\dfrac{b}{c}.](https://tex.z-dn.net/?f=%5Clog%20_ab-%5Clog_ac%3D%5Clog_a%5Cdfrac%7Bb%7D%7Bc%7D.)
For the given expression you get
![\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Clog_w%5Cdfrac%7B%28x%5E2-6%29%5E4%7D%7B%5Csqrt%5B3%5D%7Bx%5E2%2B8%7D%20%7D%3D%5Clog_w%28x%5E2-6%29%5E4-%5Clog_w%5Csqrt%5B3%5D%7Bx%5E2%2B8%7D%3D%5Clog_w%28x%5E2-6%29%5E4-%5Clog_w%28x%5E2%2B8%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
Now use property of logarithms
![\log_ab^k=k\log_ab.](https://tex.z-dn.net/?f=%5Clog_ab%5Ek%3Dk%5Clog_ab.)
For your simplified expression, you get
![\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).](https://tex.z-dn.net/?f=%5Clog_w%28x%5E2-6%29%5E4-%5Clog_w%28x%5E2%2B8%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%5Clog_w%28x%5E2-6%29-%5Cdfrac%7B1%7D%7B3%7D%5Clog_w%28x%5E2%2B8%29.)
Answer:
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
A equals 8
B eqauls 8
C equals-8
D equals 8
Answer:
Step-by-step explanation:
1/5 + 1/5^-2
1/5 + 1/25
1/5 = 5*1 / 5*5
5/25 + 1/25
6/25 which cannot be reduced or changed.