Answer:
Check pdf
Step-by-step explanation:
Try plotting the points on a graph, it might make it a bit easier to figure out an equation
The graph on the top right is non linear bc it breaks pattern in y column
Use this property of logarithms:
![\log_b\left(\dfrac{x}{y}\right)=\log_b x-\log_b y](https://tex.z-dn.net/?f=%5Clog_b%5Cleft%28%5Cdfrac%7Bx%7D%7By%7D%5Cright%29%3D%5Clog_b%20x-%5Clog_b%20y)
Your equation transforms into:
![log_4\left(\dfrac{x^2+3x}{x+5}\right)=1](https://tex.z-dn.net/?f=log_4%5Cleft%28%5Cdfrac%7Bx%5E2%2B3x%7D%7Bx%2B5%7D%5Cright%29%3D1)
Now, you have to apply the definition of a logarithm to express the equation in exponential form:
![\dfrac{x^2+3x}{x+5} = 4^1](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2B3x%7D%7Bx%2B5%7D%20%3D%204%5E1)
In case you don't remember, this is the definition of a logarithm:
![\log_b x = y \iff b^y = x](https://tex.z-dn.net/?f=%5Clog_b%20x%20%3D%20y%20%5Ciff%20b%5Ey%20%3D%20x)
The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).
Finally, solve the rational equation:
![\dfrac{x^2+3x}{x+5} =4 \iff x^2+3x=4(x+5)](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2B3x%7D%7Bx%2B5%7D%20%3D4%20%5Ciff%20x%5E2%2B3x%3D4%28x%2B5%29%20)
![\iff x^2-x-20=0](https://tex.z-dn.net/?f=%5Ciff%20x%5E2-x-20%3D0%20)
![\iff x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot(-20)}}{2}= \left \{ {{5} \atop {-4}} \right.](https://tex.z-dn.net/?f=%5Ciff%20x%3D%5Cdfrac%7B1%5Cpm%5Csqrt%7B%28-1%29%5E2-4%5Ccdot%28-20%29%7D%7D%7B2%7D%3D%20%5Cleft%20%5C%7B%20%7B%7B5%7D%20%5Catop%20%7B-4%7D%7D%20%5Cright.%20)
The correct answer is d.
Answer:
The average number of trials required to get the first success