Question

Explain why x=-8 is not part of the domain of the function y=log2(x)

Answer 1

See Below.

Explanation:

By the definition of the logarithm, if we have:

`y=\log_(2)x`

This means that we have some value y such that:

`\displaystyle 2^y=x`

If x is -8, then:

`2^y=-8`

As you can see, there is no real value* that can make the result negative. No matter what the value of y is, we will simply get another positive value.

So, -8 or any other negative value or zero is not included in our domain. 0 is not included because, likewise, we can’t raise 2 to a power and get 0 as a result.

*There is no real value for which 2 raised to y is -8. However, as you will learn much much later, there are in fact infinitely many complex (imaginary) solutions such that 2 raised to y is indeed -8.