Question

6. (5 points) What is 3loga + logb − logc written as a single logarithm?

Answer 1

Answer:
`log((a^3b)/(c))`

Explanation:

You need to use the following Properties of Logarithms:

`1)m*log(a)=log(a)^m\\\\2)log(a)+log(b)=log(ab)\\\\3)log(a)-log(b)=log((a)/(b))`

Given the following expression:

`3log(a) + log(b) - log(c)`

You can follow these steps in order to write it as a single logarightm:

- Apply the first property shown above:

`=log(a)^3 + log(b) - log(c)`

- Apply the second property:

`=log(a^3b)- log(c)`

- Finally, apply the third property:

`=log((a^3b)/(c))`