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

User Wasabi Fan
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1 Answer

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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))

User Joris Groosman
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