(a) We can expand log x5y z to get log5(xy)−log5(z) Incorrect: Your answer

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(a) We can expand 
log
x5y
z
 to get
log5(xy)−log5(z)
 
.


(b) We can combine 

5 log x + log y − log z to get
 
.
Jul 17th, 2015

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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