# Which is the domain of the function y = log 3 ( 2^x - 16 ) ?

hala718 | Certified Educator

y= log 3 (2^x - 16)

We know that the domain of y are all x values where y is defined.

The lorarithm is defined if 2^x - 16 > 0

==> 2^x - 16 >0

==> 2^x > 16

==> 2^x > 2^4

==> x > 4

Then the domain is when x belongs to the interval (4, inf)

giorgiana1976 | Student

The domain of the given function is restrictive. We'll determine the domain of the function by imposing the constraints of existance of logarithm function.

2^x - 16 > 0

We'll isolate x to the left side.

We'll add 16 both sides and we'll get:

2^x > 16

We'll write 16 as a power of 2 and we'll have:

16 = 2^4

We'll re-write the inequality:

2^x > 2^4

Because the bases ar matching, we can apply the one to one property of logarithms. Because the base is >1, the direction of the inequality remains unchanged.

x > 4

The domain of definition of the function y = log 3 ( 2^x - 16 ) is the interval (4 , +infinite).

neela | Student

y = log3 (2^x-16).

To find the domain of x.

Solution:

The image  set y is real  as long as log3 (2^x -16)  is real.

Therefore the antilog y = 2^x-16 should be positive.

2^x -16 > 16

x log2 > 16

x > log16/log2 = 4

So x > 4.

Or the domain of x is  ] 4, infinity [, which means x > 4. x not equal to 4.