The definition of log is by the equivalence:
[tex]y=log_{b}x[/tex] means [tex]b^y=x[/tex] where b>0 and b ≠ 1.
a.[tex]y=log_{10}x[/tex] is not a logarithmic function because the base is greater than 0.
False: By definition, the base of a log MUST be greater than zero but cannot equal one.
b. [tex]y=log_{\sqrt3}x[/tex] is not a logarithmic function because the base is a square root.
False: sqrt(3) is a positive number not equal to one, so it is a legitimate base.
c. [tex]y=log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.
True. Log cannot have a base of one, by definition.
Recall the definition of log where b^y=x. If b=1, b^y will also equal 1, so cannot equal x which has a domain of 0<x< ∞
d. [tex]y=log_{\frac{3}{4}}x[/tex] is not a logarithmic function because the base is a fraction.
False, because 3/4 is a legitimate base, just like any other positive number other than one.
