Question

Can someone please help me solve this logarithm equation

Answer 1

Answer:

$x=\frac{33}{7}$

Step-by-step 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:
$x=\frac{33}{7}$

Hope this helps! :3