Question

Which statement is true? a.y=log 10 x is nota logarithmic function because the base is greater than 0. b. y=log sqrt 3 xis not a logarithmic function because the base is a square root. c. y=log1xis not a logarithmic function because the base is equal to 1. d. y=log3/4 x is not a logarithmic function because the base is a fraction.

Answer 1

The definition of log is by the equivalence: 
 $y=log_{b}x$ means $b^y=x$  where b>0 and b ≠ 1.

a.$y=log_{10}x$ 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. $y=log_{\sqrt3}x$ 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. $y=log_{1}x$ 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. $y=log_{\frac{3}{4}}x$ 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.

Answer 2

Answer:

the third option is correct

Step-by-step explanation: