Answer:
4
Step-by-step explanation:
To find an equivalent expression to [tex]\sf \log_c(16) \cdot \log_2(c) [/tex], we can use the properties of logarithms, specifically the change of base formula:
[tex]\sf \log_a(b) = \dfrac{\log_c(b)}{\log_c(a)} [/tex]
Given [tex]\sf \log_c(16) [/tex], we can rewrite it in terms of base 2 using the change of base formula:
[tex]\sf \log_c(16) = \dfrac{\log_2(16)}{\log_2(c)} [/tex]
Now, we multiply it by [tex]\sf \log_2(c) [/tex]:
[tex]\sf \log_c(16) \cdot \log_2(c) = \left( \dfrac{\log_2(16)}{\log_2(c)} \right) \cdot \log_2(c) [/tex]
[tex]\sf = \log_2(16) [/tex]
[tex]\sf = \log_2(2^4) [/tex]
[tex]\sf = 4 [/tex]
So, the expression equivalent is: 4
