Question

expand the logarithm. assume all expressions exist and are w
write your answer as a sum or difference of base-r logarithms
logarithms. the inside of each logarithm must be a distinct co
\log_{r}2e

Explanation:

Step1: Recall logarithm product rule

The product rule for logarithms states that \(\log_b(xy)=\log_b x+\log_b y\) for any positive real numbers \(x\), \(y\), and \(b>0\), \(b
eq1\).

Step2: Apply the product rule to \(\log_r(2e)\)

Here, \(x = 2\) and \(y=e\) and the base \(b = r\). So, by the product rule:
\(\log_r(2e)=\log_r 2+\log_r e\)

Answer:

\(\log_{r}2 + \log_{r}e\)