IDNLearn.com: Your trusted platform for finding reliable answers. Join our interactive community and get comprehensive, reliable answers to all your questions.

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 :

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]