Question

score on last try: 2.67 of 4 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. next question get a similar question you can retry this question below the product property of logarithms works as follows: \\(\log_b(m \cdot n) = \log_b(m) + \log_b(n)\\) use this property to rewrite each of the following as a sum of logarithms. do not use the change of base formula. answers should be exact, not decimal approximations. \\(\ln(gk) = \ln(g) + \ln(k)\\) \\(\log_{36}(7wm) = \log_{30}(7) + \log_{30}(w) + \log_{30}(m)\\) \\(\log(elbow \cdot banana) = \log(elbow) + \log(banana)\\) note: \\(\log_b(a)\\) can be written using an underscore like this: \\(log\\_b(a)\\). question help: video submit question

Explanation:

Step1: Recall Log Product Property

The product property of logarithms is $\log_{b}(m \cdot n)=\log_{b}(m)+\log_{b}(n)$. For $\log_{36}(7wm)$, the base is 36, and the argument is the product $7 \times w \times m$.

Step2: Apply the Property

Using the product property, we split the logarithm of the product into the sum of logarithms with the same base (36). So $\log_{36}(7wm)=\log_{36}(7)+\log_{36}(w)+\log_{36}(m)$.

Answer:

$\log_{36}(7) + \log_{36}(w) + \log_{36}(m)$