Answer:
![x=\frac{1}{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B8%7D)
Step-by-step explanation:
A quick review on PEMDAS, the order of how to solve an equation:
P - parentheses. When parentheses are being used, you have to do everything inside them before doing everything outside of them.
E - exponents. We'll skip these, since there aren't any exponents we need to worry about in this equation.
M/D - multiplication/division. I include these both together because they can be done at the same time.
A/S = addition/subtraction. Can also be done at the same time.
Some other things to note:
You add all the things with an x attached to it, and you add all the things without an x attached to it, and these never cross.
When you bring something from one side of an equal sign to another, you make it negative.
Let's solve for x using what we've learned:
![2(1-8x)=\frac{1}{2} (8-64x)\\2-16x=4-32x\\16x=2\\x=\frac{2}{16} \\x=\frac{1}{8}](https://tex.z-dn.net/?f=2%281-8x%29%3D%5Cfrac%7B1%7D%7B2%7D%20%288-64x%29%5C%5C2-16x%3D4-32x%5C%5C16x%3D2%5C%5Cx%3D%5Cfrac%7B2%7D%7B16%7D%20%5C%5Cx%3D%5Cfrac%7B1%7D%7B8%7D)
A because is adding then subtracting then diving but last of all multiple times).))/)/)/)
3 + 4x - 3x = 4 Given
3 + (4x - 3x) = 4
3 + x = 4 Combine like terms
3 - 3 + x = 4 - 3
x = 1 Subtraction Property of Equality
The asymptote is ![x=-3](https://tex.z-dn.net/?f=x%3D-3)
Domain is ![(-3, \infty)](https://tex.z-dn.net/?f=%28-3%2C%20%5Cinfty%29)
Range is ![(-\infty, \infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20%5Cinfty%29)
Explanation:
Given that the function is ![y=\log _{3}(x+3)](https://tex.z-dn.net/?f=y%3D%5Clog%20_%7B3%7D%28x%2B3%29)
<u>Asymptote:</u>
The function has no horizontal asymptote.
The given function is of the form,
has a vertical asymptote ![x=-h](https://tex.z-dn.net/?f=x%3D-h)
where ![h=3](https://tex.z-dn.net/?f=h%3D3)
Thus, the vertical asymptote is ![x=-3](https://tex.z-dn.net/?f=x%3D-3)
<u>Domain:</u>
The domain of the function is the set of all independent x - values for which the function is real and well defined.
Let us find the positive values for log
Thus, we have,
![x+3>0](https://tex.z-dn.net/?f=x%2B3%3E0)
![x>-3](https://tex.z-dn.net/?f=x%3E-3)
Thus, the function domain in interval notation is ![(-3, \infty)](https://tex.z-dn.net/?f=%28-3%2C%20%5Cinfty%29)
<u>Range:</u>
The range of the function is the set of all dependent y - values of the function.
Hence, the range of the function is ![(-\infty, \infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20%5Cinfty%29)