Recall the change of base formula of logarithms:
[tex]\log _ax_{}=\frac{\log x}{\log a}=\frac{\ln x}{\ln a}=\frac{\log _bx}{\log _ba}[/tex]
Note that here, b can be any base.
Using this property, it follows that the given expression can be written as:
[tex]\frac{\ln8}{\ln4}=\frac{\log8}{\log4}=\frac{\log_58}{\log_54}=\log _48[/tex]
Hence, the first, second, and fourth choices are correct.
Other expressions are not equivalent expressions.
Choose the first, second, and fourth choices.
