We're given the following function:
![f(x)=log(.75^x)=log[ (\frac{3}{4}) ^{x}]=log( \frac{3^x}{4^x})](https://tex.z-dn.net/?f=f%28x%29%3Dlog%28.75%5Ex%29%3Dlog%5B%20%20%28%5Cfrac%7B3%7D%7B4%7D%29%20%5E%7Bx%7D%5D%3Dlog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%20%20)
In order to see if the function is decreasing we'll take its derivative. If
the function is increasing, if
the function is decreasing.
We take the derivate:
![\frac{d}{dx}[log( \frac{3^x}{4^x})]= \frac{4^x}{3^x}[ \frac{d}{dx} (\frac{3^x}{4^x})]=\frac{4^x}{3^x} \frac{4^x[ \frac{d}{dx} (3^x)]-3^x[ \frac{d}{dx} (4^x)]}{ 4^2^x}=](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5Blog%28%20%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%20%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28%5Cfrac%7B3%5Ex%7D%7B4%5Ex%7D%29%5D%3D%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%20%5Cfrac%7B4%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%283%5Ex%29%5D-3%5Ex%5B%20%5Cfrac%7Bd%7D%7Bdx%7D%20%284%5Ex%29%5D%7D%7B%204%5E2%5Ex%7D%3D)
![\frac{4^x}{3^x} \frac{4^x[3^xlog(3)]-3^x[4^x[4^xlog(4)]}{ 4^2^x}=log(3)-log(4)\ \textless \ 0](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ex%7D%7B3%5Ex%7D%20%5Cfrac%7B4%5Ex%5B3%5Exlog%283%29%5D-3%5Ex%5B4%5Ex%5B4%5Exlog%284%29%5D%7D%7B%204%5E2%5Ex%7D%3Dlog%283%29-log%284%29%5C%20%5Ctextless%20%5C%200)
Which implies the function is decreasing.
Another way to answer the problem (although less insightful) you can take any two real numbers
and
such that
, then if
the function is increasing and if
the function is decreasing. You can verify the function is decreasing with any two numbers in the function's domain.
Answer:
![\displaystyle 4\sqrt[7]{x^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%204%5Csqrt%5B7%5D%7Bx%5E3%7D)
General Formulas and Concepts:
<u>Algebra I</u>
- Exponential Rule [Root Rewrite]:
![\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<u>Step 2: Rewrite</u>
- Split:
- Rewrite [Exponential Rule - Root Rewrite]:
Answer: False, Vigilantes were citizens who formed committees to protect themselves. They took the law into their own hands and often acted as the judge, police, jury, and sometimes executioner.
Answer: florida circuit court
Step-by-step explanation:
Based on the information given, the Florida court that she should file her legal action against the driver is the Florida circuit court.
The Florida Circuit Court is a state court where cases such as civil cases, felony, juvenile cases, family law and probate issues are heard. Therefore, based on the scenario given, the Florida circuit court will be applicable here.
Answer:
y = -x - 1
Step-by-step explanation:
y = mx + b
<u>slope (m):</u> Since the line is going downhill, the slope will be negative
slope = rise / run
slope = 1 / 1
slope = 1
m = -1
<u>y - intercept (b):</u> this when x = 0, the line is crossing the vertical line (y-axis)
b = -1
so y = mx + b is
b = -1, m = -1
y = (-1)x + (-1)
