Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.