Which is equal to log2 0.5? Select the correct answer below: 0.5 -0.5 2 -2 -1
The Correct Answer and Explanation is:
The correct answer is: -1
Explanation:
We are asked to evaluate:
log₂(0.5)
This means:
“To what power must 2 be raised to get 0.5?”
In other words:
2^x = 0.5
Now think about the relationship between 2 and 0.5.
We know that:
2^(-1) = 1 / 2 = 0.5
Therefore:
x = -1
So:
log₂(0.5) = -1
Why this is true:
The logarithm function is the inverse of the exponential function. So when we take a logarithm, we are asking the exponent that gives us a certain number.
In general, for any base bbb and positive number aaa:logb(a)=xif and only ifbx=a\log_b(a) = x \quad \text{if and only if} \quad b^x = alogb(a)=xif and only ifbx=a
Here, our base is 2 and our number is 0.5. Since 0.5 is less than 1, the logarithm will be negative. That’s because any base raised to a negative exponent gives a fraction between 0 and 1.
Let’s verify the other choices quickly:
- 0.5: 20.5≈1.412^{0.5} \approx 1.4120.5≈1.41, which is greater than 0.5, so not correct
- -0.5: 2−0.5≈0.7072^{-0.5} \approx 0.7072−0.5≈0.707, not equal to 0.5
- 2: 22=42^2 = 422=4, incorrect
- -2: 2−2=1/4=0.252^{-2} = 1/4 = 0.252−2=1/4=0.25, too small
- -1: 2−1=1/2=0.52^{-1} = 1/2 = 0.52−1=1/2=0.5, correct
Final Answer:
log₂(0.5) = -1 ✅
