The government of a large city needs to determine whether the city's residents will support the construction of a new gymnasium
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Logarithmic functions and exponential functions are inverse and opposite of one another
The logarithmic function is , and the length at 8 pascals is 3 units
The exponential function is given as:
Express f(x) as y
Swap the positions of x and y
Take the logarithm of both sides
Apply the rule of logarithm
Divide both sides by log(2)
Apply the change of base rule of logarithm
When the strength is 8 pascals, we have:
Express 8 as 2^3
So, we have:
Evaluate log 2 base 2
Hence, the logarithmic function is , and the length at 8 pascals is 3 units
Read more about logarithmic and exponential functions at:
Answer:
k = 9
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to 8
m =
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, k)
m = = k - 1 = 8 ( add 1 to both sides )
k = 9