Answer:
[tex]x=\frac{33}{7}[/tex]
Step-by-step explanation:
Orginal equation:
[tex]log_2(x+1)-log_2(x-4)=3[/tex]
So lets do this step by step.
First, lets add [tex]log_2(x-4)[/tex] to both sides of the equation!
This gives us:
[tex]log_2(x+1)=3+log_2(x-4)[/tex]
Then, when we put this into exponential form, we get:
[tex]2^{3+log_2\left(x-4\right)}=\left(x+1\right)[/tex]
This then equals:
[tex]8(x-4) = x-1[/tex]
This can be simplfied into:
[tex]8x-32 = x+1[/tex]
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:
[tex]7x=33[/tex]
Finally, we can divide 33 by 7 to get:
[tex]x=\frac{33}{7}[/tex]
Hope this helps! :3
