Thank you for the opportunity to help you with your question!

We just need to use the following logaritmic properties:

1) log(AB) = log(A) + log(B)

2) Log(A/B) = log(A) - log(B)

3) Log(x^n) = n*log(x)

Part a

log(x^5y/z) = log(x^5y) - log(z) .................... See property 2

log(x^5y) - log(z) = log(x^5) + log(y) - log(z) ........................ See property 1

log(x^5) + log(y) - log(z) = 5log(x) + log(y) - log(z) ............... See property 3

Final answer: We can expand log(x^5y/z) to get: 5log(x) + log(y) - log(z)

Part b

5log(x) + log(y) - log(z) = log(x^5) + log(y) - log(z) ................ See property 3

log(x^5) + log(y) - log(z) = log(x^5y) - log(z) ........................... See property 1

log(x^5y) - log(z) = log(x^5y/z) ................................................. See property 2

Final answer: We can combine 5log(x) + log(y) - log(z) to get: log(x^5y/z)

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up