Answer:
![x=\frac{33}{7}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B33%7D%7B7%7D)
Step-by-step explanation:
Orginal equation:
![log_2(x+1)-log_2(x-4)=3](https://tex.z-dn.net/?f=log_2%28x%2B1%29-log_2%28x-4%29%3D3)
So lets do this step by step.
First, lets add
to both sides of the equation!
This gives us:
![log_2(x+1)=3+log_2(x-4)](https://tex.z-dn.net/?f=log_2%28x%2B1%29%3D3%2Blog_2%28x-4%29)
Then, when we put this into exponential form, we get:
![2^{3+log_2\left(x-4\right)}=\left(x+1\right)](https://tex.z-dn.net/?f=2%5E%7B3%2Blog_2%5Cleft%28x-4%5Cright%29%7D%3D%5Cleft%28x%2B1%5Cright%29)
This then equals:
![8(x-4) = x-1](https://tex.z-dn.net/?f=8%28x-4%29%20%3D%20x-1)
This can be simplfied into:
![8x-32 = x+1](https://tex.z-dn.net/?f=8x-32%20%3D%20x%2B1)
Then we can add 32 to both sides, and subtract x from both sides to get the variable and number each on their owns ide:
![7x=33](https://tex.z-dn.net/?f=7x%3D33)
Finally, we can divide 33 by 7 to get:
![x=\frac{33}{7}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B33%7D%7B7%7D)
Hope this helps! :3