Question

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

Explanation:

Step1: Recall logarithm product rule

The product rule for logarithms states that for the same base \( v \) (where \( v>0, v
eq1 \)), \( \log_v a+\log_v b = \log_v(ab) \).

Step2: Apply the rule to the given expression

We have the expression \( \log_v u+\log_v w \). Using the product rule of logarithms, we combine these two logarithms into a single logarithm by multiplying the arguments \( u \) and \( w \). So, \( \log_v u+\log_v w=\log_v(uw) \).

Answer:

\( \log_{v}(uw) \)