Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Use the product property of logarithms to write the logarithm as a sum of logarithms.

[tex]\[ \log_7[(x + y) \cdot z] = \][/tex]

[tex]\[ \log_7(x + y) + \log_7(z) \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's tackle the problem step-by-step to convert the given logarithm into the sum of logarithms using the product property.

Given:
[tex]\[ \log_7[(x + y) \cdot z] \][/tex]

We need to express this logarithm as a sum of simpler logarithms. We'll use the product property of logarithms, which states:
[tex]\[ \log_b(M \cdot N) = \log_b(M) + \log_b(N) \][/tex]

Here, [tex]\( b = 7 \)[/tex], [tex]\( M = x + y \)[/tex], and [tex]\( N = z \)[/tex].

Applying the product property, we get:
[tex]\[ \log_7[(x + y) \cdot z] = \log_7(x + y) + \log_7(z) \][/tex]

Therefore, the logarithm expressed as a sum of logarithms is:
[tex]\[ \boxed{\log_7[(x + y) \cdot z] = \log_7(x + y) + \log_7(z)} \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.