Question

for any positive numbers a, b, and d, with b ≠ 1, \\(\log_{b} a + \log_{b} d = \\) ______.

a. \\(\log_{b} a - \log_{b} d\\)

b. \\(\log_{b} a \bullet \log_{b} d\\)

c. \\(\log_{b}(a \bullet d)\\)

d. \\(d \bullet \log_{b} a\\)

Explanation:

Step1: Recall Logarithm Product Rule

The logarithm product rule states that for positive numbers \(a\), \(b\) (where \(b
eq1\)), and \(c\), \(\log_b a+\log_b c = \log_b(ac)\).

Step2: Apply the Rule to the Problem

In the given problem, we have \(\log_b a+\log_b d\). Using the logarithm product rule (where \(c = d\) in the general rule), we get \(\log_b a+\log_b d=\log_b(a\cdot d)\).

Answer:

C. \(\log_{b}(a\cdot d)\)