Help solving this please. I am unsure how to do it?
Determine the domain of the following functions, write answer using interval notation.
P( x )=log2(3x-8)
we can only take logs of positive numbers
so 3x-8 > 0
3x > 8
x > 8/3
I will let you write it in the new-fangled notation.
In my time we used the above simple way of stating it.
the domain of log(u) is u>0, regardless of the base of the logs. So, you need
3x-8 >0
x > 8/3
or,
(8/3,∞)
To determine the domain of the function P(x) = log2(3x-8), we need to consider the restrictions on the input variable x that would cause the function to be undefined.
In this case, the function is a logarithmic function with a base of 2. Logarithmic functions are undefined for zero or negative values inside the logarithm. So, the expression 3x - 8 must be greater than zero for the function to be defined.
To find the domain, we set 3x - 8 > 0 and solve for x:
3x - 8 > 0
3x > 8
x > 8/3
So, the domain of the function P(x) = log2(3x-8) is all real numbers greater than 8/3.
In interval notation, we can represent the domain as (8/3, +∞). The parentheses indicate that 8/3 is not included in the domain, and the plus sign with infinity represents all values greater than 8/3.