Question

Write the following as a single logarithm.

Please help me!!

Answer 1

`log_(i)(3c)/(7)`

Explanation:

The problems focus on two rules of logs known as the product rule and the quotient rule.

The product rule states that the log of a product of two values is equivalent to the sum of logs of single values:

`log_(a)(bc)=log_(a)b+log_(a)c`

The quotient rule states that the log of a quotient of two terms is equivalent to the difference of logs of single values:

`log_(a)((b)/(c))=log_(a)b-log_(a)c`

Since we have the same base for all three logs, we can combine them using the two rules:

`log_(i)(3)+log_(i)(c)-log_(i)(7)\\ log_(i)(3c)-log_(i)(7)\\ log_(i)((3c)/(7))`