Answer:
![y = \frac{1}{4} \times {2}^{x} - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%20%20%7B2%7D%5E%7Bx%7D%20%20-%201)
Step-by-step explanation:
Assuming the given logarithmic equation is
![y = \log_{2}( {4}{x } - 4)](https://tex.z-dn.net/?f=y%20%3D%20%20%20%5Clog_%7B2%7D%28%20%7B4%7D%7Bx%20%7D%20%20-%204%29%20)
We interchange x and y to get:
![x= \log_{2}( {4}{y} - 4)](https://tex.z-dn.net/?f=x%3D%20%20%20%5Clog_%7B2%7D%28%20%7B4%7D%7By%7D%20-%204%29%20)
We solve for y now:
![{2}^{x} = {4}{y} - 4](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bx%7D%20%20%3D%20%20%7B4%7D%7By%7D%20%20%20-%204)
We add 4 to both sides to get;
![{2}^{x} + 4 = 4y](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bx%7D%20%20%2B%204%20%3D%204y)
Divide through by 4:
![y = \frac{1}{4} \times {2}^{x} - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%20%20%7B2%7D%5E%7Bx%7D%20%20-%201)
Answer:
![1 \div {3}^{( 30)}](https://tex.z-dn.net/?f=1%20%5Cdiv%20%7B3%7D%5E%7B%28%2030%29%7D%20)
Step-by-step explanation:
There are exponent rules I posted above that are being used here.
We have (3^-6)^-5
Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.
So, we're left with 3^-30.
If you look at the photo, there's a rule for negative exponents.
Take the inverse of the base number, so 3 in this case:
1 / 3
and then make the exponent positive after taking the inverse.
So, we should get 1 / 3^30
Hope this helps!
The solution of the system can be x - 3y = 4 only if both the equations can be simplified to x - 3y = 4.
This will mean that both the equations will result in the same line which is x - 3y = 4 and thus have infinitely many solutions.
Second equation is:
Qx - 6y = 8
Taking 2 common we get:
(Q/2)x - 3y = 4
Comparing this equation to x- 3y = 4, we can say that
Q/2 = 1
So,
Q = 2
Therefore, the second equation will be:
2x - 6y = 8
First let's write it out with just numbers
6×![10^{5}](https://tex.z-dn.net/?f=10%5E%7B5%7D)
Now solve!
Solve exponent first
10^5 = 100,000
Now multiply
6 x 100,000 = 600,000
600,000 is your answer