Question

rewrite the logarithmic expression as a single logarithm with the same base. expressions exist and are well - defined. \\(\log v + \log w^{8} + \log u\\)

Explanation:

Step1: Recall log addition rule

The logarithmic property for addition is $\log_a M + \log_a N = \log_a (M \times N)$. We apply this to the given terms. First, consider $\log v + \log w^8$. By the rule, this becomes $\log (v \times w^8)$.

Step2: Add the third log term

Now, we add $\log u$ to $\log (v w^8)$. Using the same addition rule, $\log (v w^8) + \log u = \log (v w^8 \times u)$.

Step3: Rearrange the product

We can rearrange the product inside the logarithm as $\log (u v w^8)$ (since multiplication is commutative, $u \times v \times w^8 = u v w^8$).

Answer:

$\log (u v w^8)$