Answer:
a) 2
b) 5
c) -1
d) x
Step-by-step explanation:
We know the properties of log function as:
1) log(AB) = log(A) + log(B)
2) 
3) log(aᵇ) = b × log(a)
also,
4) 
Given:
a. y = log₂(2²)
thus, using 3
y = 2log₂(2)
or using 4
y = 2 × 
or
y = 2 × 1 = 2
b. y = log₂(2⁵)
thus, using 3
y = 5 × log₂(2)
or using 4
y = 5 ×
or
y = 5 × 1 = 5
c. y = log₂(2⁻¹)
thus, using 3
y = -1 × log₂(2)
or using 4
y = -1 ×
or
y = -1 × 1 = -1
d. y = log₂(2ˣ)
thus, using 3
y = x × log₂(2)
or using 4
y = x ×
or
y = x × 1 = x
<span>The canyon starts at an elevation of (-14.5). After each year, the elevation drops by (-1.5). The equation that could be written for this, then, would be (-14.5 - 1.5x = -31). First, we could add 14.5 to both sides of the equation to isolate the unknown. This would leave -1.5x = -16.5. Next, we can remove the negative signs so both sides of the equation are positive and easier to work with. This leaves 1.5x = 16.5. Finally, dividing both sides by 1.5 gives us "x = 11", which means that after 11 years, the canyon floor will be at -31 feet.</span>
