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vodka [1.7K]
3 years ago
7

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

Mathematics
1 answer:
Masteriza [31]3 years ago
3 0

Answer:

See Below.

Step-by-step explanation:

By the definition of the logarithm, if we have:

y=\log_{2}x

This means that we have some value <em>y</em> such that:

\displaystyle 2^y=x

If <em>x</em> is -8, then:

2^y=-8

As you can see,<em> </em>there is no real value* that can make the result negative. No matter what the value of <em>y</em> 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 <em>real</em> value for which 2 raised to <em>y</em> is -8. However, as you will learn much much later, there are in fact <em>infinitely</em> many <em>complex </em>(imaginary) solutions such that 2 raised to <em>y </em>is indeed -8.

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