Question

which of the following is equivalent to \\(\log_{c}(16) \cdot \log_{2}(c)\\)? choose 1 answer: a 4 b 8 c \\(\log(8)\\) d \\(\log_{c}(4)\\)

Explanation:

Step1: Apply change of base formula

$\log_{c}(16) = \frac{\log_{2}(16)}{\log_{2}(c)}$

Step2: Substitute into original expression

$\frac{\log_{2}(16)}{\log_{2}(c)} \cdot \log_{2}(c) = \log_{2}(16)$

Step3: Evaluate the logarithm

$\log_{2}(16) = \log_{2}(2^4) = 4$

Answer:

A. 4