Question

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

Answer 1

Answer: $log(\frac{a^3b}{c})$

Step-by-step explanation:

You need to use the following Properties of Logarithms:

$1)m*log(a)=log(a)^m\\\\2)log(a)+log(b)=log(ab)\\\\3)log(a)-log(b)=log(\frac{a}{b})$

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:

$=log(\frac{a^3b}{c})$