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
2 answers:
The definition of log is by the equivalence:
means 
where b>0 and b ≠ 1.
a.
<span> 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. </span>
<span> 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. </span>
<span>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. </span>
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.
a.
False: By definition, the base of a log MUST be greater than zero but cannot equal one.
b. </span>
False: sqrt(3) is a positive number not equal to one, so it is a legitimate base.
c. </span>
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. </span>
False, because 3/4 is a legitimate base, just like any other positive number other than one.
You might be interested in
For a quadratic of the form 
, we have the quadratic formula
,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
, we can get that 
, and 
. We substitute these numbers into the quadratic formula above.
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the
symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the