We need to first find a common denominator. This means that we need the 12 and the 3 to be the same number. We can change the 1/3 into 4/12 and see that 9/12 is larger than 4/12.
Answer:
The base is: ![3 \sqrt[3]{4}](https://tex.z-dn.net/?f=3%20%5Csqrt%5B3%5D%7B4%7D)
Step-by-step explanation:
Given
![f(x) = \frac{1}{4}(\sqrt[3]{108})^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%28%5Csqrt%5B3%5D%7B108%7D%29%5Ex)
Required
The base
Expand 108
![f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%28%5Csqrt%5B3%5D%7B3%5E3%20%2A%204%7D%29%5Ex)
Rewrite the exponent as:
![f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%283%5E3%20%2A%204%29%5E%5Cfrac%7B1%7D%7B3%7D%5Ex)
Expand
![f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%283%5E3%5E%5Cfrac%7B1%7D%7B3%7D%20%2A%204%5E%5Cfrac%7B1%7D%7B3%7D%29%5Ex)
![f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%283%20%2A%204%5E%5Cfrac%7B1%7D%7B3%7D%29%5Ex)
Rewrite as:
![f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%283%20%5Csqrt%5B3%5D%7B4%7D%29%5Ex)
An exponential function has the following form:
![f(x)=ab^x](https://tex.z-dn.net/?f=f%28x%29%3Dab%5Ex)
Where
![b \to base](https://tex.z-dn.net/?f=b%20%5Cto%20base)
By comparison:
![b =3 \sqrt[3]{4}](https://tex.z-dn.net/?f=b%20%3D3%20%5Csqrt%5B3%5D%7B4%7D)
So, the base is: ![3 \sqrt[3]{4}](https://tex.z-dn.net/?f=3%20%5Csqrt%5B3%5D%7B4%7D)
Answer:
x = -6
Step-by-step explanation:
Answer:
any number for example:574
Step-by-step explanation:
Depends on what the answer choices are