Answer: The correct option is (c) [tex]\dfrac{4}{3}.[/tex]
Step-by-step explanation: We are to select the correct value that is equivalent to the following expression :
[tex]E=\log_8{16}.[/tex]
We will be using the following logarithmic properties :
[tex](i)~\log a^b=b\log a,\\\\(ii)~\log_ab=\dfrac{\log b}{\log a}.[/tex]
So, the given expression becomes
[tex]E\\\\=\log_8{16}\\\\\\=\dfrac{\log16}{\log8}\\\\\\=\dfrac{\log2^4}{\log2^3}\\\\\\=\dfrac{4\log2}{3\log2}\\\\\\=\dfrac{4}{3}.[/tex]
Thus, the required value is [tex]\dfrac{4}{3}.[/tex]
Option (c) is CORRECT.
