Answer:
Option 3 - [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.
Step-by-step explanation:
To find : Which statement is true?
Solution :
As the function defined in all statement is logarithmic function.
So, The definition of logarithmic function is defined as
[tex]y=\log_bx\Rightarrow b^y=x[/tex] where, b>0 and b ≠ 1.
Now, The following statement
1) [tex]y=\log_{10}x[/tex] is not a logarithmic function because the base is greater than 0.
The statement is False as by definition, the base of a log must be greater than zero but cannot equal one.
2) [tex]y=\log_{\sqrt3}x[/tex] is not a logarithmic function because the base is a square root.
The statement is False as by definition, the base [tex]\sqrt3[/tex] is a positive number not equal to one.
3) [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.
The statement is True as by definition log cannot have a base of one.
4) [tex]y=\log_{\frac{3}{4}}x[/tex] is not a logarithmic function because the base is a fraction.
The statement is False, as 3/4 is a legitimate base, just like any other positive number other than one.
Therefore, Option 3 is true.
