Question

Can someone please help me solve this logarithm equation

Answer 1

`x=(33)/(7)`

Explanation:

Orginal equation:

`log_2(x+1)-log_2(x-4)=3`

So lets do this step by step.

First, lets add
`log_2(x-4)` to both sides of the equation!

This gives us:

`log_2(x+1)=3+log_2(x-4)`

Then, when we put this into exponential form, we get:

`2^(3+log_2\left(x-4\right))=\left(x+1\right)`

This then equals:

`8(x-4) = x-1`

This can be simplfied into:

`8x-32 = x+1`

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`

Finally, we can divide 33 by 7 to get:

`x=(33)/(7)`

Hope this helps! :3