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 third option is correct

Explanation:

Answer 2

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_{(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.